Real-variable methods in harmonic analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Mineola, N.Y.
Dover Publication
2004
|
| Edition: | 1. Dover ed.; unabridged republ. |
| Subjects: | |
| Online Access: | http://www.loc.gov/catdir/enhancements/fy0615/2003070050-d.html Inhaltsverzeichnis |
| Item Description: | Originally published: Orlando : Academic Press, 1986, in series: Pure and applied mathematics. |
| Physical Description: | XII, 462 S. |
| ISBN: | 0486435083 |
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MARC
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| 100 | 1 | |a Torchinsky, Alberto |e Verfasser |0 (DE-588)1046391348 |4 aut | |
| 245 | 1 | 0 | |a Real-variable methods in harmonic analysis |c Alberto Torchinsky |
| 250 | |a 1. Dover ed.; unabridged republ. | ||
| 264 | 1 | |a Mineola, N.Y. |b Dover Publication |c 2004 | |
| 300 | |a XII, 462 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Originally published: Orlando : Academic Press, 1986, in series: Pure and applied mathematics. | ||
| 650 | 4 | |a Harmonic analysis | |
| 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 |
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| 856 | 4 | |a Publisher description |u http://www.loc.gov/catdir/enhancements/fy0615/2003070050-d.html | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017124484 | ||
Record in the Search Index
| _version_ | 1804138627963289600 |
|---|---|
| adam_text | Contents
Preface
Chapter I Fourier Series
1.
Fourier Series of Functions
1
2.
Fourier Series of Continuous Functions
8
3.
Elementary Properties of Fourier Series
13
4.
Fourier Series of Functional
16
5.
Notes; Further Results and Problems
22
Chapter II
Cesàro Summability
1.
(C,
1)
Summability
28
2.
Fejer s Kernel
29
3.
Characterization of Fourier Series of Functions
and Measures
34
4.
A.E. Convergence of (C,
1)
Means of Summable
Functions
41
5.
Notes; Further Results and Problems
43
Chapter III Norm Convergence of Fourier Series
1.
The Case L T) Hubert Space
48
2.
Norm Convergence in
¿ (7), 1 <
ρ
<
oo
51
3.
The Conjugate Mapping
52
4.
More on
Integrable
Functions
54
5.
Integral Representation of the Conjugate Operator
59
6.
The Truncated
Hüben
Transform
65
7.
Notes; Further Results and Problems
68
Contents
Chapter IV The Basic Principles
1.
The
Calderón-Zygimmd
Interval Decomposition
74
2.
The Hardy-Littlewood Maximal Function
76
3.
The
Calderón-Zygmund
Decomposition
84
4.
The Marcinkiewicz Interpolation Theorem
86
5.
Extrapolation and the Zygmund
L
In
L
Class
91
6.
The Banach Continuity Principle and a.e. Convergence
94
7.
Notes; Further Results and Problems
100
Chapter V The Hubert Transform and Multipliers
1.
Existence of the Hilbert Transform of
Integrable
Functions
110
2.
The Hilbert Transform in L (T),
1
«S p
<
o°
115
3.
Limiting Results
121
4.
Multipliers
126
5.
Notes; Further Results and Problems
132
Chapter VI Paley s Theorem and Fractional Integration
1.
Paley s Theorem
142
2.
Fractional Integration
150
3.
Multipliers
156
4.
Notes; Further Results and Problems
158
Chapter
VII
Harmonic and Subharmonic Functions
1.
Abel Summabfflty, Nontangential Convergence
167
2.
The
Poisson
and Conjugate
Poisson
Kernels
171
3.
Harmonic Functions
176
4.
Further Properties of Harmonic Functions and
Subharmonic Functions
181
5.
Harnack s and Mean Value Inequalities
187
6.
Notes; Further Results and Problems
191
Chapter
VIII
Oscillation of Functions
1.
Mean Oscillation of Functions
199
2.
The Maximal Operator and BMO
204
3.
The Conjugate of Bounded and BMO Functions
206
4.
Wk-L and K,. Interpolation
209
5.
Lipschitz and Morrey Spaces
213
6.
Notes; Further Results and Problems
216
Contents ix
Chapter IX
Ap
Weights
1.
The Hardy-Littlewood Maximal Theorem for Regular
Measures
223
2.
Ap Weights and the Hardy-Littlewood Maximal Function
225
3.
At Weights
228
4.
Ap Weights,
ρ
> 1 233
5.
Factorization of Ap Weights
237
6.
Ap and BMO
240
7.
An Extrapolation Result
242
8.
Notes; Further Results and Problems
247
Chapter X More about R
1.
Distributions. Fourier Transforms
259
2.
Translation Invariant Operators. Multipliers
263
3.
The Hubert and Riesz Transforms
266
4.
Sobolev and
Poincaré
Inequalities
270
Chapter XI
Calderón-Zygmund
Singular
Integral Operators
1.
The
Benedek-Calderón-Panzone
Principle
280
2.
A Theorem of
Zó
282
3.
Convolution Operators
284
4.
Cotlar s Lemma
285
5.
Calderón-Zygmund
Singular Integral Operators
286
6.
Maximal
Calderón-Zygmund
Singular Integral Operators
291
7.
Singular Integral Operators in L°°(R-)
294
8.
Notes; Further Results and Problems
295
Chapter
XII
The Littlewood-Paley Theory
1.
Vector-Valued Inequalities
303
2.
Vector-Valued Singular Integral Operators
307
3.
The Littlewood-Paley
g
Function
309
4.
The Lusin Area Function and the Littlewood-Paley g*
Function
314
5.
Hörmander s
Multiplier Theorem
318
6.
Notes; Further Results and Problems
321
Chapter
XIII
The Good
λ
Principle
1.
Good
λ
Inequalities
328
Contents
2.
Weighted Norm Inequalities for Maximal CZ Singular
Integral Operators
330
3.
Weighted Weak-Type
(1,1)
Estimates for CZ Singular
Integral Operators
334
4.
Notes; Further Results and Problems
337
Chapter
XIV
Hardy Spaces of Several Real Variables
1.
Atomic Decomposition
340
2.
Maximal Function Characterization of Hardy Spaces
350
3.
Systems of Conjugate Functions
356
4.
Multipliers
359
5.
Interpolation
363
6.
Notes; Further Results and Problems
366
Chapter XV
Carleson
Measures
1.
Carleson
Measures
372
2.
Duals of Hardy Spaces
374
3.
Tent Spaces
378
4.
Notes; Further Results and Problems
383
Chapter
XVI
Cauchy Integrals on Lipschitz Carves
1.
Cauchy Integrals on Lipschitz Curves
392
2.
Related Operators
408
3.
The T Theorem
412
4.
Notes; Further Results and Problems
416
Chapter
XVII
Boundary Value Problems on C1-Domains
1.
The Double and Single Layer Potentials on a C -Domain
424
2.
The Dirichlet and Neumann Problems
438
3.
Notes
444
Bibliography
446
Index
457
|
| any_adam_object | 1 |
| author | Torchinsky, Alberto |
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| edition | 1. Dover ed.; unabridged republ. |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:31:12Z |
| institution | BVB |
| isbn | 0486435083 |
| language | English |
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| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | XII, 462 S. |
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| spelling | Torchinsky, Alberto Verfasser (DE-588)1046391348 aut Real-variable methods in harmonic analysis Alberto Torchinsky 1. Dover ed.; unabridged republ. Mineola, N.Y. Dover Publication 2004 XII, 462 S. txt rdacontent n rdamedia nc rdacarrier Originally published: Orlando : Academic Press, 1986, in series: Pure and applied mathematics. Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Publisher description http://www.loc.gov/catdir/enhancements/fy0615/2003070050-d.html Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017124484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Torchinsky, Alberto Real-variable methods in harmonic analysis Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | Real-variable methods in harmonic analysis |
| title_auth | Real-variable methods in harmonic analysis |
| title_exact_search | Real-variable methods in harmonic analysis |
| title_full | Real-variable methods in harmonic analysis Alberto Torchinsky |
| title_fullStr | Real-variable methods in harmonic analysis Alberto Torchinsky |
| title_full_unstemmed | Real-variable methods in harmonic analysis Alberto Torchinsky |
| title_short | Real-variable methods in harmonic analysis |
| title_sort | real variable methods in harmonic analysis |
| topic | Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Harmonic analysis Harmonische Analyse |
| url | http://www.loc.gov/catdir/enhancements/fy0615/2003070050-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017124484&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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