Fourier analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2001
|
| Series: | Graduate studies in mathematics
29 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Span. übers. |
| Physical Description: | XVIII, 222 S. |
| ISBN: | 0821821725 9780821821725 |
Staff View
MARC
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| 100 | 1 | |a Duoandikoetxea, Javier |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Análisis de Fourier |
| 245 | 1 | 0 | |a Fourier analysis |c Javier Duoandikoetxea. Transl. and rev. by David Cruz-Uribe |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2001 | |
| 300 | |a XVIII, 222 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 29 | |
| 500 | |a Aus dem Span. übers. | ||
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| 830 | 0 | |a Graduate studies in mathematics |v 29 |w (DE-604)BV009739289 |9 29 | |
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Record in the Search Index
| _version_ | 1804128591310487552 |
|---|---|
| adam_text | Contents
Preface
xiii
Preliminaries
xvii
Chapter
1.
Fourier Series and Integrals
1
§1.
Fourier coefficients and series
1
§2.
Criteria for pointwise convergence
2
§3.
Fourier series of continuous functions
6
§4.
Convergence in norm
8
§5.
Summability methods
9
§6.
The Fourier transform of L1 functions
11
§7.
The Schwartz class and tempered distributions
12
§8.
The Fourier transform on Lp,
1 <
ρ
< 2 15
§9.
The convergence and summability of Fourier integrals
17
§10.
Notes and further results
19
Chapter
2.
The Hardy-Littlewood Maximal Function
25
§1.
Approximations of the identity
25
§2.
Weak-type inequalities and almost everywhere convergence
26
§3.
The Marcinkiewicz interpolation theorem
28
§4.
The Hardy-Littlewood maximal function
30
ix
x
Contents
§5.
The dyadic maximal function
32
§6.
The weak
(1,1)
inequality for the maximal function
35
§7.
A weighted norm inequality
37
§8.
Notes and further results
38
Chapter
3.
The Hubert Transform
49
§1.
The conjugate
Poisson
kernel
49
§2.
The principal value of
І/ж
50
§3.
The theorems of M. Riesz and Kolmogorov
51
§4.
Truncated integrals and pointwise convergence
55
§5.
Multipliers
58
§6.
Notes and further results
61
Chapter
4.
Singular Integrals (I)
69
§1.
Definition and examples
69
§2.
The Fourier transform of the kernel
70
§3.
The method of rotations
73
§4.
Singular integrals with even kernel
77
§5.
An operator algebra
80
§6.
Singular integrals with variable kernel
83
§7.
Notes and further results
85
Chapter
5.
Singular Integrals (II)
91
§1.
The
Calderón-Zygmund
theorem
91
§2.
Truncated integrals and the principal value
94
§3.
Generalized
Calderón-Zygmund
operators
98
§4.
Calderón-Zygmund
singular integrals
101
§5.
A vector-valued extension
105
§6.
Notes and further results
107
Chapter
6.
Я1
and
В
MO
115
§1.
The space atomic H1
115
§2.
The space BMO
117
Contents xi
§3. An
interpolation
result
121
§4.
The John-Nirenberg inequality
123
§5.
Notes and further results
126
Chapter
7.
Weighted Inequalities
133
§1.
The Ap condition
133
§2.
Strong-type inequalities with weights
137
§3.
A weights and an extrapolation theorem
140
§4.
Weighted inequalities for singular integrals
143
§5.
Notes and further results
147
Chapter
8.
Littlewood-Paley Theory and Multipliers
157
§1.
Some vector-valued inequalities
157
§2.
Littlewood-Paley theory
159
§3.
The
Hörmander
multiplier theorem
163
§4.
The Marcinkiewicz multiplier theorem
166
§5.
Bochner-Riesz multipliers
168
§6.
Return to singular integrals
172
§7.
The maximal function and the Hubert transform along a
parabola
178
§8.
Notes and further results
184
Chapter
9.
The Tl Theorem
195
§1.
Cotlar s lemma
195
§2.
Carleson
measures
197
§3.
Statement and applications of the Tl theorem
201
§4.
Proof of the Tl theorem
205
§5.
Notes and further results
212
Bibliography
217
Index
219
|
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| id | DE-604.BV013771832 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:51:41Z |
| institution | BVB |
| isbn | 0821821725 9780821821725 |
| language | English |
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| oclc_num | 440695024 |
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| physical | XVIII, 222 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Duoandikoetxea, Javier Verfasser aut Análisis de Fourier Fourier analysis Javier Duoandikoetxea. Transl. and rev. by David Cruz-Uribe Providence, RI American Math. Soc. 2001 XVIII, 222 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 29 Aus dem Span. übers. Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Cruz-Uribe, David V. Sonstige (DE-588)105925235X oth Erscheint auch als Online-Ausgabe 978-1-4704-1145-9 Graduate studies in mathematics 29 (DE-604)BV009739289 29 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009413262&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Duoandikoetxea, Javier Fourier analysis Graduate studies in mathematics Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4023453-8 |
| title | Fourier analysis |
| title_alt | Análisis de Fourier |
| title_auth | Fourier analysis |
| title_exact_search | Fourier analysis |
| title_full | Fourier analysis Javier Duoandikoetxea. Transl. and rev. by David Cruz-Uribe |
| title_fullStr | Fourier analysis Javier Duoandikoetxea. Transl. and rev. by David Cruz-Uribe |
| title_full_unstemmed | Fourier analysis Javier Duoandikoetxea. Transl. and rev. by David Cruz-Uribe |
| title_short | Fourier analysis |
| title_sort | fourier analysis |
| topic | Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Harmonische Analyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009413262&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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