Garnett J.B. — Bounded Analytic Functions :: Электронная библиотека попечительского совета мехмата МГУ

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Garnett J.B. — Bounded Analytic Functions

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Название: Bounded Analytic Functions

Автор: Garnett J.B.

Аннотация:

This 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...Each chapter ends with a section called Notes and another called Exercises and further results. The former sections contain brief historical comments and direct the reader to the original sources for the material in the text.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2006

Количество страниц: 459

Добавлена в каталог: 19.06.2008

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Предметный указатель

Interpolating Blaschke products, perturbations of      301 395
Interpolating functions      9 132 145 159 284 308
Interpolating functions, parametrizations of      155 164
Interpolating sequences      184 208 275
Interpolating sequences and or BMO      307
Interpolating sequences and $\beta \mathbb{N}$       207 412 433
Interpolating sequences and analytic discs      395 404 429
Interpolating sequences and general kernels      433
Interpolating sequences and harmonic functions      293 411
Interpolating sequences, closures of      370 430
Interpolating sequences, harmonic      293
Interpolating sequences, perturbations of      301 395
Interpolation problem      145 159 275
Interpolation problem, finite      7 132 284
Interpolation, linear operator of      285
Invariant subspace of       79
Invariant subspace of and       94
Invertibility      176
Invertible function      63
Invertible function in $H^{\infty} + C$       385
Isometry      235
Isomorphic Banach space      234
Jensen formula      52
Jensen’s Inequality      33
John — Nirenberg theorem      223
Jones’s construction      349
Julia’s lemma      411
Jump theorem      85 123
Khinchin’s inequality      293 307
Kolmogoroff, theorems of      118 122 171
Koszul complex      354
Laplacian, weak      46
Least harmonic majorant      36
Least harmonic majorant and Nevanlinna class      66
Lebesgue set      44
Lebesgue’s theorem      21
Level curves      361
Lindeloef’s theorem      88
Linear operator of interpolation      285
Linearization      124
Lipschitz classes      102 121
Lipschitz condition      87
Littlewood — Paley identity      228 239 262 314 373
Littlewood — Paley integrals      228 233 259 268 343 371
Littlewood’s theorem on subharmonic functions      94
Locally integrable function      215
Logarithmic capacity      75 273
Logarithmic potential      75
Logmodular algebra      63 194 211
Marcinkiewicz interpolation theorem      25
Marshall’s theorem      189
Martingale S-function      343
Maximal conjugate function      106 see
Maximal function, dyadic      267
Maximal function, Hardy — Littlewood      21 23 246 327
Maximal function, Hardy — Littlewood, logarithm of      271
Maximal function, Hardy — Littlewood, of measure      28
Maximal function, nontangental      see Nontangental maximal function
Maximal function, vertical      116 324
Maximal Hilbert transform      123 256
Maximal ideal      83 177
Maximal ideal space      178
Maximal ideal space of $H^{\infty}$       181—182 314 391—395 419
Maximal ideal space of $l^{\infty}$       180
Maximal ideal space of a Douglas algebra      365—366
Maximal ideal space of disc algebra      207
Mean value property      10
Minimum modulus, theorems on      323 357 360 361
Minkowski inequality for integrals      14
Moduli of functions      63
Modulus of continuity      101 134
Moebius transformation      1
Mooney’s theorem      199
Morera’s theorem      91
Muckenhoupt’s theorem      247 260
Multiplicative linear functional      176
N      see Nevanlinna class
Net      192
Nevanlinna class      66 72 93 94
Nevanlinna’s theorem      145
Newman’s theorem      187
Nontangential limits      28 90 91 379
Nontangential limits and Douglas algebras      382
Nontangential limits of functions      55
Nontangential limits of functions, characterizations of      56 84
Nontangential limits of functions, moduli of      61 63
Nontangential limits of conjugate functions      99
Nontangential limits of inner functions      78
Nontangential limits of Poisson integrals of measures      29
Nontangential limits of singular functions      73
Nontangential limits of subharmonic functions      96
Nontangential limits on Lebesgue set      44
Nontangential maximal function      27 420
Nontangential maximal function and       55 111
Nontangential maximal function and N      93
Nontangential maximal function, characterizes       111
Nontangential oscillation      29
Nontangential point      428
Nontangentially bounded      90 379
Nontangentially dense      307 379
Orocycle      41 73
Orocycular point      459
Orthogonal measure      131 196 198 212
Orthogonal measure, real      213
Outer factor      71 74 172
Outer functions      64 65 81 84 94 140 142 150 151 154 155
Outer functions and dual extremal functions      171
Outer functions and extreme points      151

Outer functions and invariant subspaces      81
Paley — Wiener theorem      84
Paley’s inequality      264
Parametrizations of cosets      155
Parametrizations of interpolation functions      155 164
Partial sums of Fourier series      104 122
Peak interpolation set      120
Peak point      182
Peak set      120 121 199 208
Phragmen — Lindeloef argument      331
Pick’s Theorem      2 7 38—39
Plessner point      91
Plessner’s theorem      91
Poincare metric      4
Point of density      90
Poisson integral      10—19
Poisson integral formula      11
Poisson integral, characterization      17
Poisson integral, mean convergence of      15
Poisson kernels      10—12
Poisson kernels, approximate relations between      410
Poisson kernels, Fourier transform of      60
Pommerenke’s theorem      273
Potential, Green’s      75 94
Potential, logarithmic      75
Predual of $H^{\infty}$       198—205 213
Predual of $H^{\infty}$ , uniqueness of      203
Privalov’s theorem      91
Pseudohyperbolic distance      2 392
QC      368 386
Quadratic form      7
Quasi-continuous function      368
Range set      77
Representing measure      193
Representing measure and Douglas algebras      365
Representing measure and subharmonicity inequality      211
Representing measure, uniqueness on $H^{\infty}$       195
Riemann surface      48 430
Riesz decomposition theorem for subharmonic functions      47 96
Riesz factorization theorem      53
Riesz, F. and M., theorem      59 62 90 120 128
Riesz, F. and M., theorem, generalized      196
Riesz, M., theorem      104 108 122
Rudin, theorem of      120
Schur’s Theorem      38 175
Schwarz’s lemma      1
Semigroup property      13
Separated sequence      276 406 429
Shift operator      78
Silov boundary      182 184 208
Silov boundary and Blaschke products      187
Silov boundary and Douglas algebras      365
Silov boundary and Gleason parts      394 429
Silov boundary and interpolating Blaschke products      328
Silov boundary of $H^{\infty}$       184
Singular function      70
Singular function, boundary behavior      73
Smirnov’s theorem      71 83
Spectral radius formula      206
Spectrum      178
Stein — Weiss theorem      110 118 123
Stone — Cech compactification, $\beta \mathbb{N}$       180 395
Stone — Cech compactification, $\beta \mathbb{N}$ , and interpolating sequences      412 433
Stopping time arguments      225 328 372 see
Strong boundary point      208 394
Strongly logmodular algebra      63
Subharmonic function      32—38 45 46 94—97
Subharmonicity inequality      32 61
Subharmonicity inequality for representing measures      211
Sweep      221
Szegoe’s theorem      139
Tent      31
Top half of Q, T (Q)      286
translate      15
Triangle inequality for pseudohyperbolic distance      4
Uniform algebra      179
Uniform algebra on Y      180
Unimodular function      145 153 172 187 189 210 365 366 376
Univalent function      273 274 see
Upper half plane      5
Upper semicontinuous function      32
Vanishing mean oscillation      see VMO
Variational argument      287
Varopoulos extension      268 353
Vertical maximal function      116 324
VMO      172 242—246 368 386
VMO and Carleson measures      268
VMO and conjugate functions      245
VMO and Littlewood — Paley integrals      268
VMO      375 388 432
VMO and conjugate functions      378
VMO, dual space of      268
Weak function      20
Weak convergence in       199
Weak Laplacian      46
Weak-star convergence      15
Weak-star topology on $H^{\infty}$       82
Weak-type 1-1      23
Weakly continuous functional      200
Weight function      171 246—259
Wermer’s maximality theorem      207 366
Whitney decomposition      257
Wiener’s theorem      206
Wolff, theorem of      312 319 357
Zero set      120 122
Ziskind’s theorem      328 357
Zygmund class $\Lambda^*$       273 432
Zygmund’s theorem      110 118 122

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