Bounded Analytic FunctionsThis book is an account of the theory of Hardy spaces in one dimension, with emphasis on some of the exciting developments of the past two decades or so. The last seven of the ten chapters are devoted in the main to these recent developments. The motif of the theory of Hardy spaces is the interplay between real, complex, and abstract analysis. While paying proper attention to each of the three aspects, the author has underscored the effectiveness of the methods coming from real analysis, many of them developed as part of a program to extend the theory to Euclidean spaces, where the complex methods are not available. |
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Contents
III | 1 |
IV | 5 |
V | 10 |
VI | 19 |
VII | 27 |
VIII | 32 |
IX | 38 |
X | 39 |
XLIV | 228 |
XLV | 234 |
XLVI | 242 |
XLVII | 246 |
XLVIII | 259 |
XLIX | 261 |
L | 275 |
LI | 285 |
XI | 48 |
XII | 51 |
XIII | 55 |
XIV | 61 |
XV | 66 |
XVI | 71 |
XVII | 78 |
XVIII | 83 |
XIX | 84 |
XX | 98 |
XXI | 106 |
XXII | 111 |
XXIII | 118 |
XXIV | 120 |
XXV | 127 |
XXVI | 128 |
XXVII | 134 |
XXVIII | 139 |
XXIX | 145 |
XXX | 151 |
XXXI | 159 |
XXXII | 168 |
XXXIV | 176 |
XXXV | 186 |
XXXVI | 191 |
XXXVII | 193 |
XXXVIII | 198 |
XXXIX | 205 |
XL | 206 |
XLI | 215 |
XLIII | 223 |
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Common terms and phrases
algebra analytic analytic function approximation argument assume Banach space Blaschke product boundary bounded called Carleson measure Chapter closed closure compact complex condition conjugate Consequently constant contains continuous converges Corollary defined dense depend determined disc disjoint dist dx dy equivalent estimate everywhere example Exercise exists extension factor Figure finite fixed follows given gives harmonic function harmonic majorant Hence holds implies inequality inner function interpolating sequence interval invariant Lemma length mapping means nontangential limit norm obtain operator Poisson integral positive problem proof of Theorem prove result satisfies shows singular solution space squares subharmonic subset Suppose Theorem 2.1 theory transform uniform unique unit upper half plane Write yields zeros
References to this book
Bibliographic information
| Title | Bounded Analytic Functions Volume 236 of Graduate Texts in Mathematics |
| Author | John Garnett |
| Edition | revised |
| Publisher | Springer Science & Business Media, 2006 |
| ISBN | 0387336214, 9780387336213 |
| Length | 463 pages |
| Subjects | › Mathematics / Complex Analysis Mathematics / Functional Analysis Mathematics / Mathematical Analysis |
| Export Citation | BiBTeX EndNote RefMan |