Pointwise convergence of Fourier series:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Series: | Lecture notes in mathematics
1785 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 175 S. |
| ISBN: | 3540432701 |
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MARC
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| 245 | 1 | 0 | |a Pointwise convergence of Fourier series |c Juan Arias de Reyna |
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Record in the Search Index
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| adam_text | Table of Contents
Preface v
Introduction xi
About the notation xv
Part I. Fourier series and Hilbert Transform
1. Hardy Littlewood maximal function
1.1 Introduction 3
1.2 Weak Inequality 4
1.3 Differentiability 6
1.4 Interpolation 8
1.5 A general inequality 9
2. Fourier Series
2.1 Introduction 11
2.2 Dirichlet 12
2.3 Fourier Series of Continuous Functions 15
2.4 Banach continuity principle 18
2.5 Summability 20
2.6 The Conjugate Function 24
2.7 The Hilbert transform on R 26
2.8 The conjecture of Luzin 28
3. Hilbert Transform
3.1 Introduction 31
3.2 Truncated operators on C2(R) 31
3.3 Truncated operators on £*(R) 32
3.4 Interpolation 36
3.5 The Hilbert Transform 37
3.6 Maximal Hilbert Transform 39
VIII Table of Contents
Part II. The Carleson Hunt Theorem
4. The Basic Step
4.1 Introduction 51
4.2 Carleson maximal operator 51
4.3 Local norms 53
4.4 Dyadic Partition 56
4.5 Some definitions 59
4.6 Basic decomposition 60
4.7 The first term 61
4.8 Notation a/fi 62
4.9 The second term 63
4.10 The third term 63
4.11 First form of the basic step 66
4.12 Some comments about the proof 66
4.13 Choosing the partition 77a. The norm |||/|||o 68
4.14 Basic theorem, second form 70
5. Maximal inequalities
5.1 Maximal inequalities for A(II, x) 73
5.2 Maximal inequalities for Hjf 75
6. Growth of Partial Sums
6.1 Introduction 77
6.2 The seven trick 78
6.3 The exceptional set 78
6.4 Bound for the partial sums 81
7. Carleson Analysis of the Function
7.1 Introduction 85
7.2 A musical interlude 86
7.3 The notes of / 87
7.4 The set X 89
7.5 The set S 90
8. Allowed pairs
8.1 The length of the notes 93
8.2 Well situated notes 94
8.3 The length of well situated notes 98
8.4 Allowed pairs 99
8.5 The exceptional set 100
9. Pair Interchange Theorems
9.1 Introduction 103
9.2 Choosing the shift m 103
9.3 A bound of ||/||Q 105
9.4 Selecting an allowed pair 107
Table of Contents IX
10. All together
10.1 Introduction 117
10.2 End of proof 117
Part III. Consequences
11. Some spaces of functions
11.1 Introduction 127
11.2 Decreasing rearrangement 127
11.3 The Lorentz spaces C 1^) and £p °°(/x) 130
11.4 Marcinkiewicz interpolation theorem 134
11.5 Spaces near Cl(n) 137
11.6 The spaces £ log £(/i) and £exP(/^) 141
12. The Maximal Operator of Fourier series
12.1 Introduction 145
12.2 Maximal operator of Fourier series 145
12.3 The distribution function of 5*/ 147
12.4 The operator 5* on the space £ *, 148
12.5 The operator 5* on the space £(log C)2 149
12.6 The operator S* on the space C 150
12.7 The maximal space Q 152
12.8 The theorem of Antonov 157
13. Fourier transform on the line
13.1 Introduction 163
13.2 Fourier transform 163
References 167
Comments 171
Subject Index 173
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:59:29Z |
| institution | BVB |
| isbn | 3540432701 |
| language | English |
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| physical | XVIII, 175 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Arias de Reyna, Juan Verfasser aut Pointwise convergence of Fourier series Juan Arias de Reyna Berlin [u.a.] Springer 2002 XVIII, 175 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1785 Fourier-Reihe - Konvergenz Konvergenz (DE-588)4032326-2 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Fourier-Reihe (DE-588)4155109-6 s Konvergenz (DE-588)4032326-2 s DE-604 Lecture notes in mathematics 1785 (DE-604)BV000676446 1785 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009735383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arias de Reyna, Juan Pointwise convergence of Fourier series Lecture notes in mathematics Fourier-Reihe - Konvergenz Konvergenz (DE-588)4032326-2 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| subject_GND | (DE-588)4032326-2 (DE-588)4155109-6 |
| title | Pointwise convergence of Fourier series |
| title_auth | Pointwise convergence of Fourier series |
| title_exact_search | Pointwise convergence of Fourier series |
| title_full | Pointwise convergence of Fourier series Juan Arias de Reyna |
| title_fullStr | Pointwise convergence of Fourier series Juan Arias de Reyna |
| title_full_unstemmed | Pointwise convergence of Fourier series Juan Arias de Reyna |
| title_short | Pointwise convergence of Fourier series |
| title_sort | pointwise convergence of fourier series |
| topic | Fourier-Reihe - Konvergenz Konvergenz (DE-588)4032326-2 gnd Fourier-Reihe (DE-588)4155109-6 gnd |
| topic_facet | Fourier-Reihe - Konvergenz Konvergenz Fourier-Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009735383&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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