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.

Язык:

Рубрика: Математика/Анализ/Комплексный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 467

Добавлена в каталог: 02.04.2005

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Предметный указатель

Interpolating Blaschke products, factorization of      404
Interpolating Blaschke products, maximal ideals containing      379
Interpolating Blaschke products, perturbations of      310 404
Interpolating functions      9 138 150 165 293 317
Interpolating functions, parametrizations of      161 170
Interpolating sequences      190 215 284
Interpolating sequences and or BMO      316
Interpolating sequences and $\beta\mathbb{N}$       214 422 443
Interpolating sequences and analytic discs      404 413 439
Interpolating sequences and general kernels      443
Interpolating sequences and harmonic functions      302 421 422—428
Interpolating sequences, closures of      379 442
Interpolating sequences, harmonic      302
Interpolating sequences, perturbations of      310 404
Interpolation problem      150 165 284
Interpolation problem, finite      7 138 293
Interpolation, linear operator of      294
Invariant subspace of       82
Invariant subspace of and       98
Invertibility      182
Invertible function      66
Invertible function in $H^{\infty} + C$       395
Isometry      242
Isomorphic Banach space      242
Jensen formula      54
Jensen’s Inequality      34
John — Nirenberg theorem      230
Jones’s construction      358
Julia’s lemma      43
Jump theorem      89 128
Khinchin’s inequality      302 316
Kolmogoroff, theorems of      123 128 177
Koszul complex      364
Laplacian, weak      48
Least harmonic majorant      38
Least harmonic majorant and Nevanlinna class      69
Lebesgue set      46
Lebesgue’s theorem      21
Level curves      371
Lindelof’s theorem      92
Linear operator of interpolation      294
Linearization      129
Lipschitz classes      106 127
Lipschitz condition      90
Littlewood — Paley identity      236 246 270 323 382 383
Littlewood — Paley integrals      235 240 268 276 352 381
Littlewood’s theorem on subharmonic functions      98
Locally integrable function      222
Logarithmic capacity      78 282
Logarithmic potential      78
Logmodular algebra      66 201 218
Marcinkiewicz interpolation theorem      26
Marshall’s theorem      196
Martingale S-function      352
Maximal conjugate function      110 (see also “Maximal Hilbert transform”)
Maximal function, dyadic      275
Maximal function, Hardy — Littlewood      22 24 254 336
Maximal function, Hardy — Littlewood, logarithm of      279
Maximal function, Hardy — Littlewood, of measure      29
Maximal function, nontangental      see “Nontangental maximal function”
Maximal function, vertical      121 333
Maximal Hilbert transform      128 265
Maximal ideal      86. 183
Maximal ideal space      184
Maximal ideal space of $H^{\infty}$       189 323 400—404 428
Maximal ideal space of $l^{\infty}$       186
Maximal ideal space of a Douglas algebra      374 375
Maximal ideal space of disc algebra      214
Mean value property      11
Minimum modulus, theorems on      332 367 370 371
Minkowski inequality for integrals      14
Mobius transformation      1
Moduli of functions      66
Modulus of continuity      105 140
Mooney’s theorem      206
Morera’s theorem      95
Muckenhoupt’s theorem      255 268
Multiplicative linear functional      182
N      see “Nevanlinna class”
Net      198
Nevanlinna class      69—75 97 98
Nevanlinna’s theorem      151
Newman’s theorem      194
Nontangential limits      29 94 95 389
Nontangential limits and Douglas algebras      392
Nontangential limits of functions      57
Nontangential limits of functions, characterizations of      58 88
Nontangential limits of functions, moduli of      64 66
Nontangential limits of conjugate functions      103
Nontangential limits of inner functions      81
Nontangential limits of Poisson integrals of measures      30 31 77
Nontangential limits of singular functions      76
Nontangential limits of subharmonic functions      98
Nontangential limits on Lebesgue set      46
Nontangential maximal function      28 430
Nontangential maximal function and       57 115
Nontangential maximal function and N      97
Nontangential maximal function, characterizes       115
Nontangential oscillation      30
Nontangential point      438
Nontangentially bounded      94 389
Nontangentially dense      316 389
Orocycle      43 76
Orocycular point      438
Orthogonal measure      136 203 205 219
Orthogonal measure, real      219
Outer factor      74 78 179
Outer functions      67 68 87 98 145 147 156 160 161

Outer functions and dual extremal functions      177
Outer functions and extreme points      157
Outer functions and invariant subspaces      84
Paley — Wiener theorem      88
Paley’s inequality      273
Parametrizations of cosets      160
Parametrizations of interpolation functions      161 170
Partial sums of Fourier series      108 127
Peak interpolation set      125
Peak point      189
Peak set      125 127 205 215
Phragmen — Lindelof argument      340
Pick’s Theorem      2 7 40
Plessner point      95
Plessner’s theorem      95
Poincare metric      5
Point of density      94
Poisson integral      11—20
Poisson integral formula      11
Poisson integral, characterization      18
Poisson integral, mean convergence of      15
Poisson kernels      11 12
Poisson kernels, approximate relations between      419
Poisson kernels, Fourier transform of      62
Pommerenke’s theorem      282
Potential, Green’s      78 98
Potential, logarithmic      78
Predual of $H^{\infty}$       205—212 220
Predual of $H^{\infty}$ , uniqueness of      210
Privalov’s theorem      94 389
Pseudohyperbolic distance      2 401
QC      377 378 396
Quadratic form      7
Quasi-continuous function      377
Range set      80
Representing measure      200
Representing measure and Douglas algebras      374
Representing measure and subharmonicity inequality      218
Representing measure, uniqueness on $H^{\infty}$       202
Riemann surface      51 440
Riesz decomposition theorem for subharmonic functions      49 100
Riesz factorization theorem      56
Riesz, F. and M., theorem      61 65 94 125 133
Riesz, F. and M., theorem, generalized      203
Riesz, M, theorem      108 113 128
Rudin, theorem of      125
Schur’s Theorem      40 180
Schwarz’s lemma      1
Semigroup property      14
Separated sequence      285 415 439
Shift operator      82
Silov boundary      188 191 215
Silov boundary and Blaschke products      194
Silov boundary and Douglas algebras      374
Silov boundary and Gleason parts      402 438
Silov boundary and interpolating Blaschke products      337
Silov boundary of $H^{\infty}$       191
Singular function      73
Singular function, boundary behavior      76
Smirnov’s theorem      74 87
Spectral radius formula      213
Spectrum      184
Stein — Weiss theorem      115 123 128
Stone — Cech compactification, $\beta\mathbb{N}$       186 404
Stone — Cech compactification, $\beta\mathbb{N}$ and interpolating sequences      422 443
Stopping time arguments      232 338 382
Strong boundary point      215 403
Strongly logmodular algebra      66
Subharmonic function      33—39 47 48 98—101
Subharmonicity inequality      33 64
Subharmonicity inequality for representing measures      218
Sweep      229
Szego’s theorem      144
Tent      32
Top half of Q, T(Q)      290
translate      16
Triangle inequality for pseudohyperbolic distance      4
Uniform algebra      185
Uniform algebra on Y      186
Unimodular function      151 159 179 192 195 217 374 375 386
Univalent function      281 282
Upper half plane      5
Upper semicontinuous function      33
Vanishing mean oscillation      see “VMO”
Variational argument      296
Varopoulos extension      276 362
Vertical maximal function      121 333
VMO      179 250—253 377 396
VMO and Carleson measures      276
VMO and conjugate functions      252
VMO and Littlewood — Paley integrals      276
VMO, dual space of      276
Weak function      21
Weak convergence in $L^1\H^1$       206
Weak Laplacian      48
Weak-star convergence      15
Weak-star topology on $H^{\infty}$       85
Weak-type 1-1      24
Weakly continuous functional      207
Weight function      178 254—267
Wermer’s maximality theorem      214 375
Whitney decomposition      266
Wiener’s theorem      213
Wolff, theorem of      322 324 366
Zero set      125 127
Ziskind’s theorem      337 367
Zygmund class $\Lambda^{\ast}$       282 442
Zygmund’s theorem      114 123 128

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