Bounded analytic functions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Edition: | Revised first edition |
| Series: | Graduate texts in mathematics
236 |
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBR01 UBT01 UPA01 Volltext Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource (xiv, 459 Seiten) |
| ISBN: | 9780387497631 |
| DOI: | 10.1007/0-387-49763-3 |
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Record in the Search Index
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| adam_text | Contents
Preface vii
List of Symbols xiii
I. PRELIMINARIES
1. Schwarz s Lemma 1
2. Pick s Theorem 5
3. Poisson Integrals 10
4. Hardy Littlewood Maximal Function 19
5. Nontangential Maximal Function and Fatou s Theorem 27
6. Subharmonic Functions 32
Notes 38
Exercises and Further Results 39
II. Hp SPACES
1. Definitions 48
2. Blaschke Products 51
3. Maximal Functions and Boundary Values 55
4. (l/7r)/(log|/(/)|/(l+r2))^ oo 61
5. The Nevanlinna Class 66
6. Inner Functions 71
7. Beurling s Theorem 78
Notes 83
Exercises and Further Results 84
III. CONJUGATE FUNCTIONS
1. Preliminaries 98
2. The Lp Theorems 106
3. Conjugate Functions and Maximal Functions 111
ix
X CONTENTS
Notes 118
Exercises and Further Results 120
IV. SOME EXTREMAL PROBLEMS
1. Dual Extremal Problems 128
2. The Carleson Jacobs Theorem 134
3. The Helson Szego Theorem 139
4. Interpolating Functions of Constant Modulus 145
5. Parametrization of K 151
6. Nevanlinna s Proof 159
Notes 168
Exercises and Further Results 168
V. SOME UNIFORM ALGEBRA
1. Maximal Ideal Spaces 176
2. Inner Functions 186
3. Analytic Discs in Fibers 191
4. Representing Measures and Orthogonal Measures 193
5. The Space L /^o 198
Notes 205
Exercises and Further Results 206
VI. BOUNDED MEAN OSCILLATION
1. Preliminaries 215
2. The John Nirenberg Theorem 223
3. Littlewood Paley Integrals and Carleson Measures 228
4. Fefferman s Duality Theorem 234
5. Vanishing Mean Oscillation 242
6. Weighted Norm Inequalities 245
Notes 259
Exercises and Further Results 261
VII. INTERPOLATING SEQUENCES
1. Carleson s Interpolation Theorem 275
2. The Linear Operator of Interpolation 285
3. Generations 289
4. Harmonic Interpolation 292
5. Earl s Elementary Proof 299
Notes 304
Exercises and Further Results 305
CONTENTS xi
VIII. THE CORONA CONSTRUCTION
1. Inhomogeneous Cauchy Riemann Equations 309
2. The Corona Theorem 314
3. Two Theorems on Minimum Modulus 323
4. Interpolating Blaschke Products 327
5. Carleson s Construction 333
6. Gradients of Bounded Harmonic Functions 338
7. A Constructive Solution of db/dz = fi 349
Notes 357
Exercises and Further Results 358
IX. DOUGLAS ALGEBRAS
1. The Douglas Problem 364
2. H°° + C 367
3. The Chang Marshall Theorem 369
4. The Structure of Douglas Algebras 375
5. The Local Fatou Theorem and an Application 379
Notes 384
Exercises and Further Results 385
X. INTERPOLATING SEQUENCES AND MAXIMAL IDEALS
1. Analytic Discs in OT 391
2. Hoffman s Theorem 401
3. Approximate Dependence between Kernels 406
4. Interpolating Sequences and Harmonic Separation 412
5. A Constructive Douglas Rudin Theorem 418
Notes 428
Exercises and Further Results 428
BIBLIOGRAPHY 434
INDEX 453
|
| adam_txt |
Contents
Preface vii
List of Symbols xiii
I. PRELIMINARIES
1. Schwarz's Lemma 1
2. Pick's Theorem 5
3. Poisson Integrals 10
4. Hardy Littlewood Maximal Function 19
5. Nontangential Maximal Function and Fatou's Theorem 27
6. Subharmonic Functions 32
Notes 38
Exercises and Further Results 39
II. Hp SPACES
1. Definitions 48
2. Blaschke Products 51
3. Maximal Functions and Boundary Values 55
4. (l/7r)/(log|/(/)|/(l+r2))^ oo 61
5. The Nevanlinna Class 66
6. Inner Functions 71
7. Beurling's Theorem 78
Notes 83
Exercises and Further Results 84
III. CONJUGATE FUNCTIONS
1. Preliminaries 98
2. The Lp Theorems 106
3. Conjugate Functions and Maximal Functions 111
ix
X CONTENTS
Notes 118
Exercises and Further Results 120
IV. SOME EXTREMAL PROBLEMS
1. Dual Extremal Problems 128
2. The Carleson Jacobs Theorem 134
3. The Helson Szego Theorem 139
4. Interpolating Functions of Constant Modulus 145
5. Parametrization of K 151
6. Nevanlinna's Proof 159
Notes 168
Exercises and Further Results 168
V. SOME UNIFORM ALGEBRA
1. Maximal Ideal Spaces 176
2. Inner Functions 186
3. Analytic Discs in Fibers 191
4. Representing Measures and Orthogonal Measures 193
5. The Space L'/^o 198
Notes 205
Exercises and Further Results 206
VI. BOUNDED MEAN OSCILLATION
1. Preliminaries 215
2. The John Nirenberg Theorem 223
3. Littlewood Paley Integrals and Carleson Measures 228
4. Fefferman's Duality Theorem 234
5. Vanishing Mean Oscillation 242
6. Weighted Norm Inequalities 245
Notes 259
Exercises and Further Results 261
VII. INTERPOLATING SEQUENCES
1. Carleson's Interpolation Theorem 275
2. The Linear Operator of Interpolation 285
3. Generations 289
4. Harmonic Interpolation 292
5. Earl's Elementary Proof 299
Notes 304
Exercises and Further Results 305
CONTENTS xi
VIII. THE CORONA CONSTRUCTION
1. Inhomogeneous Cauchy Riemann Equations 309
2. The Corona Theorem 314
3. Two Theorems on Minimum Modulus 323
4. Interpolating Blaschke Products 327
5. Carleson's Construction 333
6. Gradients of Bounded Harmonic Functions 338
7. A Constructive Solution of db/dz = fi 349
Notes 357
Exercises and Further Results 358
IX. DOUGLAS ALGEBRAS
1. The Douglas Problem 364
2. H°° + C 367
3. The Chang Marshall Theorem 369
4. The Structure of Douglas Algebras 375
5. The Local Fatou Theorem and an Application 379
Notes 384
Exercises and Further Results 385
X. INTERPOLATING SEQUENCES AND MAXIMAL IDEALS
1. Analytic Discs in OT 391
2. Hoffman's Theorem 401
3. Approximate Dependence between Kernels 406
4. Interpolating Sequences and Harmonic Separation 412
5. A Constructive Douglas Rudin Theorem 418
Notes 428
Exercises and Further Results 428
BIBLIOGRAPHY 434
INDEX 453 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:33:15Z |
| indexdate | 2024-07-09T20:57:42Z |
| institution | BVB |
| isbn | 9780387497631 |
| language | English |
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| spelling | Garnett, John B. 1940- Verfasser (DE-588)13370856X aut Bounded analytic functions John B. Garnett Revised first edition Berlin [u.a.] Springer 2007 1 Online-Ressource (xiv, 459 Seiten) txt rdacontent c rdamedia cr rdacarrier Graduate texts in mathematics 236 Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Analytische Funktion (DE-588)4142348-3 s Funktionalanalysis (DE-588)4018916-8 s 1\p DE-604 DE-604 Erscheint auch als Druck-Ausgabe 978-0-387-33621-3 Graduate texts in mathematics 236 (DE-604)BV035421258 236 https://nbn-resolving.org/urn:nbn:de:1111-200708029153 Verlag Volltext https://doi.org/10.1007/0-387-49763-3 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015650915&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Garnett, John B. 1940- Bounded analytic functions Graduate texts in mathematics Funktionalanalysis (DE-588)4018916-8 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4142348-3 |
| title | Bounded analytic functions |
| title_auth | Bounded analytic functions |
| title_exact_search | Bounded analytic functions |
| title_exact_search_txtP | Bounded analytic functions |
| title_full | Bounded analytic functions John B. Garnett |
| title_fullStr | Bounded analytic functions John B. Garnett |
| title_full_unstemmed | Bounded analytic functions John B. Garnett |
| title_short | Bounded analytic functions |
| title_sort | bounded analytic functions |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd Analytische Funktion (DE-588)4142348-3 gnd |
| topic_facet | Funktionalanalysis Analytische Funktion |
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