Modern Fourier analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in mathematics
250 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke, 1. Aufl. (in 1 Bd. zs. mit 1. Aufl. von Grafakos, Loukas: Classical Fourier analysis) u.d.T.: Grafakos, Loukas: Classical and modern Fourier analysis |
| Beschreibung: | XV, 504 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387094335 |
Internformat
MARC
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| 100 | 1 | |a Grafakos, Loukas |d 1962- |e Verfasser |0 (DE-588)136654444 |4 aut | |
| 245 | 1 | 0 | |a Modern Fourier analysis |c Loukas Grafakos |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XV, 504 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 250 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke, 1. Aufl. (in 1 Bd. zs. mit 1. Aufl. von Grafakos, Loukas: Classical Fourier analysis) u.d.T.: Grafakos, Loukas: Classical and modern Fourier analysis | ||
| 650 | 4 | |a Fourier analysis | |
| 650 | 4 | |a Fourier analysis |v Problems, exercises, etc | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-387-09434-2 |
| 830 | 0 | |a Graduate texts in mathematics |v 250 |w (DE-604)BV000000067 |9 250 | |
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Datensatz im Suchindex
| _version_ | 1811034388866007040 |
|---|---|
| adam_text |
Contents
Smoothness and Function Spaces
. 1
6.1
Riesz and Bessel Potentials, Fractional Integrals
. 1
6.1.1
Riesz Potentials
. 2
6.1.2
Bessel Potentials
. 6
Exercises
. 9
6.2
Sobolev Spaces
. 12
6.2.1
Definition and Basic Properties of General Sobolev Spaces
. 13
6.2.2
Littlewood-Paley Characterization of Inhomogeneous
Sobolev Spaces
. 16
6.2.3
Littlewood-Paley Characterization of Homogeneous
Sobolev Spaces
. 20
Exercises
. 22
6.3
Lipschitz Spaces
. 24
6.3.1
Introduction to Lipschitz Spaces
. 25
6.3.2
Littlewood-Paley Characterization of Homogeneous
Lipschitz Spaces
. 27
6.3.3
Littlewood-Paley Characterization of Inhomogeneous
Lipschitz Spaces
. 31
Exercises
. 34
6.4
Hardy Spaces
. 37
6.4.1
Definition of Hardy Spaces
. 37
6.4.2 Quasinorm
Equivalence of Several Maximal Functions
. 40
6.4.3
Consequences of the Characterizations of Hardy Spaces
----- 53
6.4.4
Vector-Valued Hp and Its Characterizations
. 56
6.4.5
Singular Integrals on Hardy Spaces
. 58
6.4.6
The Littlewood-Paley Characterization of Hardy Spaces
. 63
Exercises
. 66
6.5
Besov-Lipschitz and Triebel-Lizorkin Spaces
. 68
6.5.1
Introduction of Function Spaces
. 68
6.5.2
Equivalence of Definitions
. 71
Exercises
. 76
Contents
6.6
Atomie
Decomposition
. 78
6.6.1
The Space of Sequences j"'9
. 78
6.6.2
The Smooth Atomic Decomposition of Fp'4
. 78
6.6.3
The Nonsmooth Atomic Decomposition of Fp'4
. 82
6.6.4
Atomic Decomposition of Hardy Spaces
. 86
Exercises
. 90
6.7
Singular Integrals on Function Spaces
. 93
6.7.1
Singular Integrals on the Hardy Space Hl
. 93
6.7.2
Singular Integrals on Besov-Lipschitz Spaces
. 96
6.7.3
Singular Integrals on
Яр(К")
. 96
6.7.4
A Singular Integral Characterization of
Я1
(R")
.104
Exercises
.
Ill
BMO and
Carleson
Measures
.117
7.1
Functions of Bounded Mean Oscillation
.117
7.1.1
Definition and Basic Properties of BMO
.118
7.1.2
The John-Nirenberg Theorem
.124
7.1.3
Consequences of Theorem
7.1.6.128
Exercises
.129
7.2
Duality between Hl and BMO
.130
Exercises
.135
7.3
Nontangential Maximal Functions and
Carleson
Measures
.135
7.3.1
Definition and Basic Properties of
Carleson
Measures
.136
7.3.2
BMO Functions and
Carleson
Measures
.141
Exercises
.144
7.4
The Sharp Maximal Function
.146
7.4.1
Definition and Basic Properties of the Sharp Maximal
Function
.146
7.4.2
A Good Lambda Estimate for the Sharp Function
.148
7.4.3
Interpolation Using BMO
.151
7.4.4
Estimates for Singular Integrals Involving the Sharp Function
152
Exercises
.155
7.5
Commutators of Singular Integrals with BMO Functions
.157
7.5.1
An Orlicz-Type Maximal Function
.158
7.5.2
A Pointwise Estimate for the Commutator
.161
7.5.3
IP Boundedness of the Commutator
.163
Exercises
.165
Singular Integrals of Nonconvolution Type
.169
8.1
General Background and the Role of BMO
.169
8.1.1
Standard Kernels
.170
8.1.2
Operators Associated with Standard Kernels
.175
8.1.3
Calderón-Zygmund
Operators Acting on Bounded Functions
179
Exercises
.181
8.2
Consequences of L2 Boundedness
.182
Contents xiii
8.2.1
Weak Type
( 1
,
1 )
and
LP
Boundedness of Singular Integrals
183
8.2.2
Boundedness of Maximal Singular Integrals
.185
8.2.3
Я1
-> Ü
and U°
->
BMO Boundedness of Singular Integrals
188
Exercises
.191
8.3
The
7(1)
Theorem
.193
8.3.1
Preliminaries and Statement of the Theorem
.193
8.3.2
The Proof of Theorem
8.3.3.196
8.3.3
An Application
.209
Exercises
.211
8.4
Paraproducts
.212
8.4.1
Introduction to Paraproducts
.212
8.4.2
I? Boundedness of Paraproducts
.214
8.4.3
Fundamental Properties of Paraproducts
.216
Exercises
.222
8.5
An Almost Orthogonality Lemma and Applications
.223
8.5.1
The Cotlar-Knapp-Stein Almost Orthogonality Lemma
_224
8.5.2
An Application
.227
8.5.3
Almost Orthogonality and the
7(1)
Theorem
.230
8.5.4
Pseudodifferential Operators
.233
Exercises
.236
8.6
The Cauchy Integral of
Calderón
and the T(b) Theorem
.238
8.6.1
Introduction of the Cauchy Integral Operator along a
Lipschitz Curve
.239
8.6.2
Resolution of the Cauchy Integral and Reduction of Its L2
Boundedness to a Quadratic Estimate
.242
8.6.3
A Quadratic
7(1)
Type Theorem
.246
8.6.4
A T(b) Theorem and the L2 Boundedness of the Cauchy
Integral
.250
Exercises
.253
8.7
Square Roots of Elliptic Operators
.256
8.7.1
Preliminaries and Statement of the Main Result
.256
8.7.2
Estimates for Elliptic Operators on R"
.257
8.7.3
Reduction to a Quadratic Estimate
.260
8.7.4
Reduction to
a Carleson
Measure Estimate
.261
8.7.5
The T(b) Argument
.267
8.7.6
The Proof of Lemma
8.7.9.270
Exercises
.275
9
Weighted Inequalities
.279
9.1
The Ap Condition
.279
9.1.1
Motivation for theAp Condition
.280
9.1.2
Properties of Ap Weights
.283
Exercises
.291
9.2
Reverse Holder Inequality and Consequences
.293
9.2.1
The Reverse Holder Property of Ap Weights
.293
xiv Contents
9.2.2
Consequences of the Reverse Holder Property
.297
Exercises
.299
9.3
The A» Condition
.302
9.3.1
The Class of
A„
Weights
.302
9.3.2
Characterizations of A» Weights
.304
Exercises
.308
9.4
Weighted Norm Inequalities for Singular Integrals
.309
9.4.1
A Review of Singular Integrals
.309
9.4.2
A Good Lambda Estimate for Singular Integrals
.310
9.4.3
Consequences of the Good Lambda Estimate
.316
9.4.4
Necessity of the Ap Condition
.321
Exercises
.322
9.5
Further Properties of Ap Weights
.324
9.5.1
Factorization of Weights
.324
9.5.2
Extrapolation from Weighted Estimates on a Single U°
_325
9.5.3
Weighted Inequalities Versus Vector-Valued Inequalities
. 332
Exercises
.335
10
Boundedness and Convergence of Fourier Integrals
.339
10.1
The Multiplier Problem for the Ball
.340
10.1.1
Sprouting of Triangles
.340
10.1.2
The counterexample
.343
Exercises
.350
10.2
Bochner-Riesz Means and the
Carleson-Sjölin
Theorem
.351
10.2.1
The Bochner-Riesz Kernel and Simple Estimates
.351
10.2.2
The
Carleson-Sjölin
Theorem
.354
10.2.3
The Kakeya Maximal Function
.359
10.2.4
Boundedness of a Square Function
.361
10.2.5
The Proof of Lemma
10.2.5 .363
Exercises
.366
10.3
Kakeya Maximal Operators
.368
10.3.1
Maximal Functions Associated with a Set of Directions
. 368
10.3.2
The Boundedness of
ЯЯ£лг
on I/(R2)
.370
10.3.3
The Higher-Dimensional Kakeya Maximal Operator
.378
Exercises
.384
10.4
Fourier Transform Restriction and Bochner-Riesz Means
.387
10.4.1
Necessary Conditions for Rp^q(S"'1) to Hold
.388
10.4.2
A Restriction Theorem for the Fourier Transform
.390
10.4.3
Applications to Bochner-Riesz Multipliers
.393
10.4.4
The Full Restriction Theorem on R2
.396
Exercises
.402
10.5
Almost Everywhere Convergence of Bochner-Riesz Means
.403
10.5.1
A Counterexample for the Maximal Bochner-Riesz Operator404
10.5.2
Almost Everywhere Summability of the Bochner-Riesz
Means
.407
Contents xv
10.5.3
Estimates for Radial Multipliers
.411
Exercises
.419
11
Time-Frequency Analysis and the Carleson-Hunt Theorem
.423
11.1
Almost Everywhere Convergence of Fourier Integrals
.423
11.1.1
Preliminaries
.424
11.1.2
Discretization of the
Carleson
Operator
.428
11.1.3
Linearization of a Maximal Dyadic Sum
.432
11.1.4
Iterative Selection of Sets of Tiles with Large Mass and
Energy
.434
11.1.5
Proof of the Mass Lemma
11.1.8.439
11.1.6
Proof of Energy Lemma
11.1.9.441
11.1.7
Proof of the Basic Estimate Lemma
11.1.10.446
Exercises
.452
11.2
Distributional Estimates for the
Carleson
Operator
.456
11.2.1
The Main Theorem and Preliminary Reductions
.456
11.2.2
The Proof of Estimate
(11.2.8).460
11.2.3
The Proof of Estimate
(11.2.9).462
11.2.4
The Proof of Lemma
11.2.2 .463
Exercises
.474
11.3
The Maximal
Carleson
Operator and Weighted Estimates
.475
Exercises
.479
Glossary
.483
References
.487
Index
.501
About the first edition:
"Grafakos's book is very user-friendly with numerous examples illustrating the
definitions and ideas. The treatment is thoroughly modern with free use of op¬
erators and functional analysis. Morever, unlike many authors, Grafakos has
clearly spent a great deal of time preparing the exercises."
—
Kenneth Ross, MAA Online
The primary goal of these two volumes is to present the theoretical foundation
of the field of Euclidean Harmonic analysis. The original edition was published
as a single volume, but due to its size, scope, and the addition of new material,
the second edition consists of two volumes. The present edition contains a new
chapter on time-frequency analysis and the Carleson-Hunt theorem. The first
volume contains the classical topics such as Interpolation, Fourier Series, the
Fourier Transform, Maximal Functions, Singular Integrals, and Littlewood-Paley
Theory. The second volume contains more recent topics such as Function Spaces,
Atomic Decompositions, Singular Integrals of Nonconvolution Type, and
Weighted Inequalities.
These volumes are mainly addressed to graduate students in mathematics and
are designed for a two-course sequence on the subject with additional material
included for reference. The prerequisites for the first volume are satisfactory
completion of courses in real and complex variables. The second volume assumes
material from the first This book is intended to present the selected topics in
depth and stimulate further study. Although the emphasis falls on real variable
methods in EucHdean spaces, a chapter is devoted to the fundamentals of analysis
on the torus. This materiel
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| adam_txt |
Contents
Smoothness and Function Spaces
. 1
6.1
Riesz and Bessel Potentials, Fractional Integrals
. 1
6.1.1
Riesz Potentials
. 2
6.1.2
Bessel Potentials
. 6
Exercises
. 9
6.2
Sobolev Spaces
. 12
6.2.1
Definition and Basic Properties of General Sobolev Spaces
. 13
6.2.2
Littlewood-Paley Characterization of Inhomogeneous
Sobolev Spaces
. 16
6.2.3
Littlewood-Paley Characterization of Homogeneous
Sobolev Spaces
. 20
Exercises
. 22
6.3
Lipschitz Spaces
. 24
6.3.1
Introduction to Lipschitz Spaces
. 25
6.3.2
Littlewood-Paley Characterization of Homogeneous
Lipschitz Spaces
. 27
6.3.3
Littlewood-Paley Characterization of Inhomogeneous
Lipschitz Spaces
. 31
Exercises
. 34
6.4
Hardy Spaces
. 37
6.4.1
Definition of Hardy Spaces
. 37
6.4.2 Quasinorm
Equivalence of Several Maximal Functions
. 40
6.4.3
Consequences of the Characterizations of Hardy Spaces
----- 53
6.4.4
Vector-Valued Hp and Its Characterizations
. 56
6.4.5
Singular Integrals on Hardy Spaces
. 58
6.4.6
The Littlewood-Paley Characterization of Hardy Spaces
. 63
Exercises
. 66
6.5
Besov-Lipschitz and Triebel-Lizorkin Spaces
. 68
6.5.1
Introduction of Function Spaces
. 68
6.5.2
Equivalence of Definitions
. 71
Exercises
. 76
Contents
6.6
Atomie
Decomposition
. 78
6.6.1
The Space of Sequences j"'9
. 78
6.6.2
The Smooth Atomic Decomposition of Fp'4
. 78
6.6.3
The Nonsmooth Atomic Decomposition of Fp'4
. 82
6.6.4
Atomic Decomposition of Hardy Spaces
. 86
Exercises
. 90
6.7
Singular Integrals on Function Spaces
. 93
6.7.1
Singular Integrals on the Hardy Space Hl
. 93
6.7.2
Singular Integrals on Besov-Lipschitz Spaces
. 96
6.7.3
Singular Integrals on
Яр(К")
. 96
6.7.4
A Singular Integral Characterization of
Я1
(R")
.104
Exercises
.
Ill
BMO and
Carleson
Measures
.117
7.1
Functions of Bounded Mean Oscillation
.117
7.1.1
Definition and Basic Properties of BMO
.118
7.1.2
The John-Nirenberg Theorem
.124
7.1.3
Consequences of Theorem
7.1.6.128
Exercises
.129
7.2
Duality between Hl and BMO
.130
Exercises
.135
7.3
Nontangential Maximal Functions and
Carleson
Measures
.135
7.3.1
Definition and Basic Properties of
Carleson
Measures
.136
7.3.2
BMO Functions and
Carleson
Measures
.141
Exercises
.144
7.4
The Sharp Maximal Function
.146
7.4.1
Definition and Basic Properties of the Sharp Maximal
Function
.146
7.4.2
A Good Lambda Estimate for the Sharp Function
.148
7.4.3
Interpolation Using BMO
.151
7.4.4
Estimates for Singular Integrals Involving the Sharp Function
152
Exercises
.155
7.5
Commutators of Singular Integrals with BMO Functions
.157
7.5.1
An Orlicz-Type Maximal Function
.158
7.5.2
A Pointwise Estimate for the Commutator
.161
7.5.3
IP Boundedness of the Commutator
.163
Exercises
.165
Singular Integrals of Nonconvolution Type
.169
8.1
General Background and the Role of BMO
.169
8.1.1
Standard Kernels
.170
8.1.2
Operators Associated with Standard Kernels
.175
8.1.3
Calderón-Zygmund
Operators Acting on Bounded Functions
179
Exercises
.181
8.2
Consequences of L2 Boundedness
.182
Contents xiii
8.2.1
Weak Type
( 1
,
1 )
and
LP
Boundedness of Singular Integrals
183
8.2.2
Boundedness of Maximal Singular Integrals
.185
8.2.3
Я1
-> Ü
and U°
->
BMO Boundedness of Singular Integrals
188
Exercises
.191
8.3
The
7(1)
Theorem
.193
8.3.1
Preliminaries and Statement of the Theorem
.193
8.3.2
The Proof of Theorem
8.3.3.196
8.3.3
An Application
.209
Exercises
.211
8.4
Paraproducts
.212
8.4.1
Introduction to Paraproducts
.212
8.4.2
I? Boundedness of Paraproducts
.214
8.4.3
Fundamental Properties of Paraproducts
.216
Exercises
.222
8.5
An Almost Orthogonality Lemma and Applications
.223
8.5.1
The Cotlar-Knapp-Stein Almost Orthogonality Lemma
_224
8.5.2
An Application
.227
8.5.3
Almost Orthogonality and the
7(1)
Theorem
.230
8.5.4
Pseudodifferential Operators
.233
Exercises
.236
8.6
The Cauchy Integral of
Calderón
and the T(b) Theorem
.238
8.6.1
Introduction of the Cauchy Integral Operator along a
Lipschitz Curve
.239
8.6.2
Resolution of the Cauchy Integral and Reduction of Its L2
Boundedness to a Quadratic Estimate
.242
8.6.3
A Quadratic
7(1)
Type Theorem
.246
8.6.4
A T(b) Theorem and the L2 Boundedness of the Cauchy
Integral
.250
Exercises
.253
8.7
Square Roots of Elliptic Operators
.256
8.7.1
Preliminaries and Statement of the Main Result
.256
8.7.2
Estimates for Elliptic Operators on R"
.257
8.7.3
Reduction to a Quadratic Estimate
.260
8.7.4
Reduction to
a Carleson
Measure Estimate
.261
8.7.5
The T(b) Argument
.267
8.7.6
The Proof of Lemma
8.7.9.270
Exercises
.275
9
Weighted Inequalities
.279
9.1
The Ap Condition
.279
9.1.1
Motivation for theAp Condition
.280
9.1.2
Properties of Ap Weights
.283
Exercises
.291
9.2
Reverse Holder Inequality and Consequences
.293
9.2.1
The Reverse Holder Property of Ap Weights
.293
xiv Contents
9.2.2
Consequences of the Reverse Holder Property
.297
Exercises
.299
9.3
The A» Condition
.302
9.3.1
The Class of
A„
Weights
.302
9.3.2
Characterizations of A» Weights
.304
Exercises
.308
9.4
Weighted Norm Inequalities for Singular Integrals
.309
9.4.1
A Review of Singular Integrals
.309
9.4.2
A Good Lambda Estimate for Singular Integrals
.310
9.4.3
Consequences of the Good Lambda Estimate
.316
9.4.4
Necessity of the Ap Condition
.321
Exercises
.322
9.5
Further Properties of Ap Weights
.324
9.5.1
Factorization of Weights
.324
9.5.2
Extrapolation from Weighted Estimates on a Single U°
_325
9.5.3
Weighted Inequalities Versus Vector-Valued Inequalities
. 332
Exercises
.335
10
Boundedness and Convergence of Fourier Integrals
.339
10.1
The Multiplier Problem for the Ball
.340
10.1.1
Sprouting of Triangles
.340
10.1.2
The counterexample
.343
Exercises
.350
10.2
Bochner-Riesz Means and the
Carleson-Sjölin
Theorem
.351
10.2.1
The Bochner-Riesz Kernel and Simple Estimates
.351
10.2.2
The
Carleson-Sjölin
Theorem
.354
10.2.3
The Kakeya Maximal Function
.359
10.2.4
Boundedness of a Square Function
.361
10.2.5
The Proof of Lemma
10.2.5 .363
Exercises
.366
10.3
Kakeya Maximal Operators
.368
10.3.1
Maximal Functions Associated with a Set of Directions
. 368
10.3.2
The Boundedness of
ЯЯ£лг
on I/(R2)
.370
10.3.3
The Higher-Dimensional Kakeya Maximal Operator
.378
Exercises
.384
10.4
Fourier Transform Restriction and Bochner-Riesz Means
.387
10.4.1
Necessary Conditions for Rp^q(S"'1) to Hold
.388
10.4.2
A Restriction Theorem for the Fourier Transform
.390
10.4.3
Applications to Bochner-Riesz Multipliers
.393
10.4.4
The Full Restriction Theorem on R2
.396
Exercises
.402
10.5
Almost Everywhere Convergence of Bochner-Riesz Means
.403
10.5.1
A Counterexample for the Maximal Bochner-Riesz Operator404
10.5.2
Almost Everywhere Summability of the Bochner-Riesz
Means
.407
Contents xv
10.5.3
Estimates for Radial Multipliers
.411
Exercises
.419
11
Time-Frequency Analysis and the Carleson-Hunt Theorem
.423
11.1
Almost Everywhere Convergence of Fourier Integrals
.423
11.1.1
Preliminaries
.424
11.1.2
Discretization of the
Carleson
Operator
.428
11.1.3
Linearization of a Maximal Dyadic Sum
.432
11.1.4
Iterative Selection of Sets of Tiles with Large Mass and
Energy
.434
11.1.5
Proof of the Mass Lemma
11.1.8.439
11.1.6
Proof of Energy Lemma
11.1.9.441
11.1.7
Proof of the Basic Estimate Lemma
11.1.10.446
Exercises
.452
11.2
Distributional Estimates for the
Carleson
Operator
.456
11.2.1
The Main Theorem and Preliminary Reductions
.456
11.2.2
The Proof of Estimate
(11.2.8).460
11.2.3
The Proof of Estimate
(11.2.9).462
11.2.4
The Proof of Lemma
11.2.2 .463
Exercises
.474
11.3
The Maximal
Carleson
Operator and Weighted Estimates
.475
Exercises
.479
Glossary
.483
References
.487
Index
.501
About the first edition:
"Grafakos's book is very user-friendly with numerous examples illustrating the
definitions and ideas. The treatment is thoroughly modern with free use of op¬
erators and functional analysis. Morever, unlike many authors, Grafakos has
clearly spent a great deal of time preparing the exercises."
—
Kenneth Ross, MAA Online
The primary goal of these two volumes is to present the theoretical foundation
of the field of Euclidean Harmonic analysis. The original edition was published
as a single volume, but due to its size, scope, and the addition of new material,
the second edition consists of two volumes. The present edition contains a new
chapter on time-frequency analysis and the Carleson-Hunt theorem. The first
volume contains the classical topics such as Interpolation, Fourier Series, the
Fourier Transform, Maximal Functions, Singular Integrals, and Littlewood-Paley
Theory. The second volume contains more recent topics such as Function Spaces,
Atomic Decompositions, Singular Integrals of Nonconvolution Type, and
Weighted Inequalities.
These volumes are mainly addressed to graduate students in mathematics and
are designed for a two-course sequence on the subject with additional material
included for reference. The prerequisites for the first volume are satisfactory
completion of courses in real and complex variables. The second volume assumes
material from the first This book is intended to present the selected topics in
depth and stimulate further study. Although the emphasis falls on real variable
methods in EucHdean spaces, a chapter is devoted to the fundamentals of analysis
on the torus. This materiel
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| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Grafakos, Loukas 1962- |
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| bvnumber | BV035085975 |
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| callnumber-raw | QA403.5 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 990 SK 450 |
| classification_tum | MAT 420f |
| ctrlnum | (OCoLC)248979166 (DE-599)DNB988365359 |
| dewey-full | 515.2433 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.2433 |
| dewey-search | 515.2433 |
| dewey-sort | 3515.2433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035085975 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:08:56Z |
| indexdate | 2024-09-24T00:16:21Z |
| institution | BVB |
| isbn | 9780387094335 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016754156 |
| oclc_num | 248979166 |
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| physical | XV, 504 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2009 |
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| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Grafakos, Loukas 1962- Verfasser (DE-588)136654444 aut Modern Fourier analysis Loukas Grafakos 2. ed. New York, NY Springer 2009 XV, 504 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 250 Hier auch später erschienene, unveränderte Nachdrucke, 1. Aufl. (in 1 Bd. zs. mit 1. Aufl. von Grafakos, Loukas: Classical Fourier analysis) u.d.T.: Grafakos, Loukas: Classical and modern Fourier analysis Fourier analysis Fourier analysis Problems, exercises, etc Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-09434-2 Graduate texts in mathematics 250 (DE-604)BV000000067 250 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016754156&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016754156&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Grafakos, Loukas 1962- Modern Fourier analysis Graduate texts in mathematics Fourier analysis Fourier analysis Problems, exercises, etc Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | Modern Fourier analysis |
| title_auth | Modern Fourier analysis |
| title_exact_search | Modern Fourier analysis |
| title_exact_search_txtP | Modern Fourier analysis |
| title_full | Modern Fourier analysis Loukas Grafakos |
| title_fullStr | Modern Fourier analysis Loukas Grafakos |
| title_full_unstemmed | Modern Fourier analysis Loukas Grafakos |
| title_short | Modern Fourier analysis |
| title_sort | modern fourier analysis |
| topic | Fourier analysis Fourier analysis Problems, exercises, etc Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Fourier analysis Fourier analysis Problems, exercises, etc Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016754156&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016754156&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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