Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Koosis P. — Introduction to Hp Spaces (Cambridge Tracts in Mathematics)
Koosis P. — Introduction to Hp Spaces (Cambridge Tracts in Mathematics)

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Introduction to Hp Spaces (Cambridge Tracts in Mathematics)

Автор: Koosis P.

Аннотация:

The first edition of this well-known book was noted for its clear and accessible exposition of the basic theory of Hardy spaces from the concrete point of view (in the unit circle and the half plane). This second edition retains many of the features found in the first — detailed computation, an emphasis on methods — but greatly extends its coverage. The discussions of conformal mapping now include Lindelöf's second theorem and the one due to Kellogg. A simple derivation of the atomic decomposition for RH1 is given, and then used to provide an alternative proof of Fefferman's duality theorem. Two appendices by V.P. Havin have also been added: on Peter Jones' interpolation formula for RH1 and on Havin's own proof of the weak sequential completeness of L1/H1(0). Numerous other additions, emendations and corrections have been made throughout.


Язык: en

Рубрика: Математика/Анализ/Продвинутый анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1998

Количество страниц: 287

Добавлена в каталог: 02.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$Ho_{\infty}$ (space)      83
$H_1$ (space)      34ff
$H_p$      68
$H_p$ (space) for upper half plane      112
$H_{\infty}$ (space) for upper half plane      114
Adamian, Arov and Krein; their theorem      150
Approximate identity property      72
atom      188 195
Atom of $\Re H_1 (\Im z > 0)      188
Atom of $\Re H_1(|z| < 1)$      195 241
Atomic decomposition      188 223 241 242
Baire category theorem, use of      25 201 275
Beurling’s theorem on invariant subspaces      79 121 162 167
Blaschke product      65 68 69 70 76 83 84 85 120 137 152 157
BMO (space)      169 217
Bonenblust — Sobczyk theorem: its use      216
Boundary value function      15
Boundary value, non-tangential      11 57
Bounded mean oscillation      215 217
Burkholder, Gundy and Silverstein; their theorem      182
Calderon — Zygmund decomposition      192 196 237
Caratheodory’s theorem on conformal mapping      36 40 52 63
Carleson index      267
Carleson measures      197 201 202 206 209 223 229 230 244 251 256 257 260 261 262 269
Carleson property      211
Carleson’s theorem      205 207 263
Cauchy principal value      24 58 87 129
Cauchy’s formula: functions in $H_1$      35
Coifman’s theorem      194
Conjugate Poisson kernel      18
Connectivity, simple      36
Contiguous intervals      29 60
Convolution      135
Corona theorem (of Carleson)      253 258
Distribution function      92 170
Entire function of exponential type      132
Fatou’s construction      159 163
Fatou’s theorem      11
Fatou’s theorem on a.e. Existence of boundary values      57
Fefferman and Stein; their theorem      186 251
Fefferman’s theorem      240 241 243 247
Fefferman’s theorem: with Garsia’s norm      227 240
Fourier transform      131
Frostman’s theorem on uniform approximation by Blaschke products      85 157
Garnett’s theorem      211
Garsia’s norm      221
Gelfand’s theorem on complete normed fields      253
Green’s theorem, use of      223 224 233 257
Hardy — Littlewood maximal function      172 188
Hardy — Littlewood maximal theorem      172 174 176
Hardy’s theorem (on domains with rectifiable boundary)      55
Harmonic conjugate      1 16ff 87 88 89 108 109 122 163 215
Harmonic conjugate, boundary behaviour of      16ff
Harmonic extension $U_{\phi}$ of $\phi$ to unit circle      221
Harnack’s theorem      13 212
Hausdorff — Young theorem      130
Helson — Szego measure      163 166
Hilbert transform      88 104 129
Homomorphisms of the algebra $H_{\infty}$ onto $\mathbb{C}$      252
Inner factor      74 119 120 155
Inner function      82 83 84 152 153
Interpolating sequence      200 201 205 210 211 254
Invariant subspaces      81
Jensen’s formula      66 67
Jensen’s Inequality      75
John — Nirenberg theorem      236
Jones’ interpolation formula      264
Jordan curve argument      37 38 39 40
Jordan curve theorem      36 40 42
Kellogg’s theorem      103
Kolmogorov’s theorem      92
Kolmogorov’s theorem (for 0 < p < 1)      98
Lebesgue set      19
Lebesgue’s theorem (on differentiation)      15 173 236
Lindelof’s first theorem on conformal mapping      40ff
Lindelof’s second theorem on conformal mapping      48
Marcinkiewicz interpolation      94 174 175
Marshall’s theorem      157
Maximal function, Hardy — Littlewood      172 188
Maximal function, non-tangential      178 179 194 197
Maximal function, radial      186
Maximal Hilbert transform      181
Maximal ideal in $H_{\infty}$      252ff
Maximal ideal space $\mathcal{M}$ of $H_{\infty}$      253
Nirenberg and John; their theorem      235
Non-tangential      15
Non-tangential boundary value      11 57
Non-tangential convergence      11
Non-tangential limit      11 46
Non-tangential maximal function      178 179 194 197
Outer factor      78 119 120 152 155
Paley — Wiener theorem      132 134 135
Phragmen — Lindelof theorem      132
Plancherel’s theorem      131
Poisson formula      2 117 153 221
Poisson kernel      3 5 7 16 126
Poisson kernel, conjugate      17 126
Poisson kernel: approximate identity property      8 35
Poisson representation: for functions harmonic in a disk      2
Poisson representation: for harmonic functions with bounded $L_p$ means      3ff
Privalov’s construction      59ff 62
Privalov’s theorem on Lipshitzian functions      100
Privalov’s uniqueness theorem      62
Radially bounded measure      243 247
Regular functional      273
Rich (subset of $L_{\infty}$)      272 277
Riemann mapping theorem      35
Riesz theorem, F. And M.      28ff 72 115 116 142 149 158 160 216 226
Riesz’ theorem, M.      94 128
Sarason’s theorem      148
Shapiro and Shields; their theorem      207
Simple connectivity      36
Smirnov’s theorem      74
Smirnov’s theorem: generalization      79
Supporting interval      135
Szego’s theorem      161 164
Titchmarsh’s convolution theorem      138
Unimodular functions      152
Vinogradov — Senichkin test      269
Vinogradov’s characterization (of Carleson measures)      269
w-convergent (sequence)      272
Weakly complete (normed space)      272 277
Weakly convergent (sequence)      271
Weakly convergent in itself (sequence)      271
Wolff’s lemma      256
Zygmund’s L logl theorem      96
Zygmund’s theorem (converse)      97
Zygmund’s trick      72 73 80
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте