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Garnett J.B. — Bounded Analytic Functions
Garnett J.B. — Bounded Analytic Functions



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Название: Bounded Analytic Functions

Автор: Garnett J.B.

Язык: en

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
$(A_2)$ condition      258
$(A_p)$ condition      254
$(A_x)$ condition      280
$(A_{\infty})$ condition      264
$A_0$      see “Disc algebra”
$A_{\alpha}$      see “Lipschitz class”
$C_A$      316 386 388
$H^1$      50
$H^1$ and absolute continuity      61
$H^1$ and bounded variation      93
$H^1$ and cosets of $L^{\infty}/H^{\infty}$      153 160 204
$H^1$ as real Banach space      243 (see also “IF”)
$H^1$, arguments of functions in      159 179
$H^1$, atomic decomposition      274
$H^1$, dual space of      245 372
$H^1$, extreme points of ball      157
$H^1_{\mathbb{R}}$,      274
$H^2$      50 82
$H^p$      50—53 133
$H^p$ and extremal problems      132—139
$H^p$ and harmonic majorants      60
$H^p$ and interpolating sequences      316
$H^p$ and maximal functions      57 120
$H^p$ as sums of outer functions      87
$H^p$, boundary behavior      57—66 88
$H^p$, derivatives from      89
$H^p$, distance to      134
$H^p$, dual spaces      90 242 245
$H^p$, factorizations in      56 74 87
$H^p$, Fourier series of      59
$H^p$, Fourier transform of      62
$H^p$, real or positive functions in      95 138
$H^{\infty} + C$      137 178 376—378 394 396
$H^{\infty} + C$, invertible functions in      395
$H^{\infty} + C$, maximal ideals of      377
$H^{\infty}$      50 66 373
$H^{\infty}$ and Banach approximation property      212
$H^{\infty}$ as logmodular algebra      66 201
$H^{\infty}$ as uniform algebra      189—197
$H^{\infty}$ maximal ideal space      189 323 400—404 428
$H^{\infty}$, analytic structure in maximal ideal space      197—199 400—415
$H^{\infty}$, best approximation in      135 140 174 177
$H^{\infty}$, cosets of in $L^{\infty}/H^{\infty}$      151 160
$H^{\infty}$, distance to      135 137 148 248 372 386
$H^{\infty}$, exposed points of      221
$H^{\infty}$, extreme points of      179
$H^{\infty}$, ideals of      85 86 189 323 329 369
$H^{\infty}$, interpolations by      see “Interpolating functions; Interpolating sequences; Interpolation problem”
$H^{\infty}$, measures orthogonal to      136 203 205 219
$H^{\infty}$, peak sets of      205
$H^{\infty}$, predualof      205—212 220
$H^{\infty}$, representing measures for      202—205 218 374
$H^{\infty}$, Silov boundary of      191
$H^{\infty}$, weak-star closed ideals      85
$H^{\infty}$, weak-star density of polynomials      89
$H^{\infty}$, weakly continuous functionals on      205—212 220
$l^p$      12 15 33 46 58 127 133
$L^p$ and conjugate functions      108 111—113
$L^p$ and interpolating sequences      316
$L^p$ and representing measures      202
$l^{\infty}$      186
$L^{\infty}$ and conjugate functions      105 114 147 227
$l^{\infty}$, complemented in $H^{\infty}$      295
$L^{\infty}$, distance to      249 258
$l^{\infty}$, interpolation in      285
$N^{+}$      71 74 98
$Q_A$      376 385 388
$VMO_A$      385 398 442
$VMO_A$ and conjugate functions      388
$\mathcal{B}$ = set of inner functions      373
$\mathcal{B}=ballH^{\infty}$      1—10 41 43 50 165
Adamyan, Arov, and Krein theorem      151 160
Amar — Lederer lemma      205
Analytic discs      199
Analytic discs and Carleson measures      439
Analytic discs and interpolating sequences      408 413
Analytic map      198 401 414 415 441
Ando’s theorem      210 212
Angle between subspaces      146 178
Angular derivative      43 441
Approximate identity      20
atom      274
B      see “Bloch functions”
Bad function      130
Badly approximable function      177 179
Balyage      229
Banach algebra      182
Banach approximation property      212
Banach — Alaoglu theorem      19
Bernard’s theorem      195
Best approximation      135
Best approximation in $H^{\infty} + C$      396
Best approximation in $H^{\infty}$      135 140 174 177
Best approximation in Douglas algebra      396
Best approximation, continuity of      140 177
Beurling, P., theorem of      294 313
Beurling’s theorem      82
Blaschke condition      53
Blaschke products      54 55 79 80
Blaschke products and Silov boundary      194
Blaschke products as interpolating functions      9 174 309
Blaschke products, boundary continuity      75
Blaschke products, characterization      56
Blaschke products, density in inner functions      79
Blaschke products, factorizations      406 411
Blaschke products, finite      6 9 138 150 180
Blaschke products, interpolating      see “Interpolating Blaschke product”
Blaschke products, logarithms of moduli of      288
Bloch functions      282 283 442
BMO      223—235 244—250 269—283
BMO and $(A_p)$ weights      258
BMO and Carleson measure      229 240 272 273 275 327
BMO and conformal mappings      281
BMO and conjugate functions      235 248 358 361
BMO and interpolating sequences      316
BMO and Littlewood — Paley integrals      240 270
BMO as dual of $H^1_{\mathbb{R}}$      245 276 372
BMO, distance to $L^{\infty}$ in      258 281
BMO, dyadic      274
BMOA      270 281—283
Boundary      188
Boundary, Silov      see “Silov boundary”
Bounded lower oscillation      281
Bounded mean oscillation      see “BMO”
Box kernel      23 224
Burkholder, Gundy, and Silverstein theorem      116
Calderon — Zygmund lemma      231
Canonical Factorization theorem      74
Capacity      78 282
Caratheodory theorem      6 93
Carleson measures      31 63 238
Carleson measures and analytic disc      439
Carleson measures and arc length      340
Carleson measures and BMO      229 240 268 273 275 327
Carleson measures and Cauchy — Rieman equations      320 322 358
Carleson measures and conformal invariance      239
Carleson measures and gradients      240 268 273 275 346
Carleson measures and interpolating sequences      287 358
Carleson measures and Littlewood — Paley integrals      240 268
Carleson norm      31
Carleson — Jacobs theorem      140
Carleson, theorems of      33 63 125 127 191 287 324
Cauchy — Riemann equations, inhomogeneous      319
Chang — Marshall theorem      373 378 399
Chebychev inequality      21
Cluster set      80
Cluster set and fiber      216
Commutator      278
Complemented subspace      295
Complex homomorphism      182
Cone $\Gamma_{\alpha}(e^{i\varphi})$      24
Cone $\Gamma_{\alpha}(t)$      22
Conformal mappings and Bloch functions      282
Conformal mappings and BMO      281
Conformal mappings, boundary behavior      93
Conjugate functions      66 102 388
Conjugate functions and $L^1$      111 115
Conjugate functions and $L^p$      113
Conjugate functions and $L^{\infty}$      105 114 147 227
Conjugate functions and BMO      227 235 248
Conjugate functions and maximal functions      116
Conjugate functions and VMO      252 388
Conjugate functions and VMO, Hilbert transform      66 102 388
Conjugate functions in $L^2(\mu)$      149
Conjugate functions in $L^p(\mu)$      255
Conjugate functions, continuity of      106 127
Conjugate functions, maximal      110
Conjugate Poisson kernel      103 109
Conjugation operator      103
Constant of interpolation      285 293
Convolution      12 13
Corona      323
Corona data      324
Corona problem on plane domains      368
Corona solutions      324
Corona theorem      191 324
Cosets of $L^{\infty}/H^{\infty}$      151 157
Covering lemma      25
de Leeuw — Rudin theorem      157 159
Degree of finite Blaschke product      6
Derivatives of $H^p$ functions      89 273
Dilation      13
Dini continuity      105 127 140
Dirichlet algebra      201 217
Disc algebra      125 133 137 177 189 192 196 214 221 375 394 395
Disc, euclidean      3
Disc, noneuclidean      2
Distance in $L^2(\mu)$      144 177
Distance in BMO to $L^{\infty}$      249 258
Distance to $A_0$      137
Distance to $H^p$      135 175
Distance to $H^{\infty} + C$      395 396
Distance to $H^{\infty}$      135 137 148 248 372 386
Distance to $Re H^{\infty}$      249 259
Distribution function      20
Douglas algebras      373 379
Douglas algebras and VMO      385
Douglas algebras, characterizations      381 392
Douglas algebras, maximal ideal spaces      374 375
Douglas algebras, structure of      385—389
Douglas problem      373
Douglas — Rudin theorem      192 217 374 399
Douglas — Rudin theorem, constructive      428
Dual extremal function      134 136
Dual extremal problem      133 175 292
Dual space of $H^1$      245
Dual space of $H^p$      90 242
Dual space of VMO      276
Dyadic $H^1$      275
Dyadic BMO      275
Dyadic maximal function      275
Earl’s construction      308
Endomorphism of $H^{\infty}$      439
Expectation      302
Exposed point      159 221
Extremal function      139 152 160 172 175
Extremal problem, dual      133 175 292
Extremal problem, nonlinear      296
Extreme point of $ball(H^1)$      157
Extreme point of $ball(H^{\infty})$      179
Extremely disconnected space      214
Fatou theorem      29 125 348
Fatou theorem, local      94 389
Fefferman — Stein theorems      125 280
Fefferman’s theorem      245
Fefferman’s theorem, constructively      358
Fiber      190 214 395
Fiber algebra      395
Fiber and cluster set      216
Fourier multiplier      108
Fourier series      107 273
Fourier series of $H^p$ function      59
Fourier transform      62 110
Frostman theorem      79
Gehring’s inequality      260
Gelfand topology      184
Gelfand transform      184
Generates      195
Generations      299 426
Generations and corona construction      344
Generations and dependencies of kernals      417
Generations and gradients of functions      351
Generations and interpolating Blaschke products      338 (see also “Stopping time argument”)
Geodesic, hyperbolic      5 41
Gleason distance      42
Gleason parts      402
Gleason parts and analytic discs      402. 408
Gleason parts, homeomorphic to unit disc      440
Gleason parts, one point      402 413 438
Good $\lambda$ inequality      266 269
Good function      130
Gradients of harmonic functions      235 240 347 372
Gradients of harmonic functions and BMO      270 273
Greatest common divisor (of family of inner functions)      84
Greatest lower bound (of family of measures)      84
Green’s potential      78 98
Green’s Theorem      236
Hall’s lemma      367
Hardy space      see “$H^p$”
Hardy — Littlewood inequality      121
Hardy — Littlewood maximal functions      22 24 254 336
Hardy — Littlewood maximal theorem      24
Hardy’s inequality      93 273
Harmonic conjugate      66 (see also “Conjugate function”)
Harmonic function      11
Harmonic interpolating sequence      302 313 371 421
Harmonic majorant      38
Harmonic measure      13 41 367
Helson — Szego theorem      147 254 258
Hilbert transform      105 128 147 149 254 265 388 395
Hoffman’s theorem      410 413
Homogeneity of kernels      13
Homomorphism, complex      182
Hunt, Muckenhoupt, and Wheeden theorem      255 268
Ideal, generated by ${f_1, ..., f_n}$      328 369
Ideal, maximal      183
Ideal, square of      414
Ideal, weak-star closed      85
Inhomogeneous Cauchy — Riemann equations      319
Inhomogeneous Cauchy — Riemann equations and interpolating Blaschke products      358
Inner factor      78
Inner functions      75 79 80
Inner functions and $L^{\infty}$      192
Inner functions and Douglas algebras      378
Inner functions and ideals in $H^{\infty}$      85
Inner functions and invariant subspaces      82
Inner functions and Silov boundary      194
Inner functions as interpolating functions      151 172
Inner functions, approximation by Blaschke product      80
Inner functions, behavior of singularities      81
Inner functions, generating $H^{\infty}$      192
Integrable, locally      222
Interpolating Blaschke products      336 404
Interpolating Blaschke products and approximation problem      430
Interpolating Blaschke products and Douglas algebras      379 380 398
Interpolating Blaschke products and inhomogeneous Cauchy — Riemann equations      358
Interpolating Blaschke products and maximal ideal space      428
Interpolating Blaschke products and nontangential points      438
Interpolating Blaschke products and Silov boundary      337
Interpolating Blaschke products as interpolating functions      309
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