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Stein E.M. — Singular Integrals and Differentiability Properties of Functions

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Название: Singular Integrals and Differentiability Properties of Functions

Автор: Stein E.M.

Аннотация:

This book is an outgrowth of a course which I gave at Oarsay during the academic year 1966-1967.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 152

Добавлена в каталог: 19.12.2012

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Предметный указатель

$H^{p}$ spaces      220—235
$\gamma_{0,\alpha}$ , $(=(2\pi)^{-a}\gamma(\alpha))$       73 117
Almost-everywhere convergence      9 42 63
Approximation to the identity      62 see
Area integral of Lusin, also S function      89 205 224 265
Bessel potentials      130 133 149 see
Bounded mean oscillation      164
Calderon and Zygmund lemma      17
Cone      89 197
Cone, truncated      201
Conjugate harmonic functions      65 143 212
Convolutions      27
Covering lemma      9
Decomposition of open sets into cubes      16 167
Derivatives in the $L^{q}$ sense, pointwise      242
Derivatives in the harmonic sense      246
Derivatives in the weak sense      121 180 241
Derivatives, ordinary, pointwise      241
Derivatives, symmetric      268
Desymmetrization      257 265
Dilations      37 50 55 110 118
Distance function, $\delta(x)$       13 170
Distribution function      4 21 50 121 272
Domain with minimally smooth boundary      189 see
Dyadic decomposition      103
Elliptic differential operators      77 114
Extension operators, $\mathbf{E}$       193
Extension operators, $\mathfrak{G}$       182 191 194
Extension operators, $\mathscr{E}_{0}$       171
Extension operators, $\mathscr{E}_{k}$       176
Fatou's theorem      199
Fatou's theorem, local version      201
Fourier transform      28 56 71
Fractional integration      see "Riesz potentials"
Function spaces      see "Lipschitz spaces" "Potential "Sobolov
Green's theorem      69 87 208
Hardy inequalities      272
Harmonic functions      60 68 78 196—239 274—276
Hecke's identity      71
Hilbert transform      26 30 38 42 49 50 54
Integral of Marcinkiewicz involving the distance function      14 32 253
Laplacean, $\Delta$       59 60 69 117
Lebesgue, set      10 197
Lebesgue, theorem      4

Lipschitz spaces, $Lip\ (\gamma,F)$       173 176
Lipschitz spaces, $\Lambda_{\alpha}$       141 163
Lipschitz spaces, $\Lambda_{\alpha}^{p,q}$       150 161 193
Littlewood and Paley functions, $g^{*}_{\lambda}$       88 96 115 162 224 233
Littlewood and Paley functions, $g_{1}$       83 96 112 162
Littlewood and Paley functions, $g_{k}$       86
Littlewood and Paley functions, $g_{x}$       83 112
Littlewood and Paley functions, g      82 112 155
Marcinkiewicz multiplier theorem      108 114
Maximal functions      4 22—25 42 62 87 92 197 221 236
Minkowski's inequality for integrals      271
Modulus of continuity, $L^{p}$ norm      138 140
Modulus of continuity, regular      175
Multiplier transformations      28 43 75 94 108—114 232
Non-measurable sets      251
Non-tangential boundedness      201
Non-tangential convergence      197 213 236 246
Operators commuting with translations      see "Multiplier transformations"
Partial sum operator      99
Partition of unity      170
Point of density      12 251 259
Poisson integral      61 82 87 92 142 197
Poisson kernel      61 142 146 197
Potential spaces, $\mathscr{L}_{\alpha}^{p}$       135 154 161—162 192—193
Principal-value integrals      35
Rademacher functions      104 276—278
rectangle      99
Regular family      10
Regularization      123
Regularized distance      170 182
Restriction to linear sub-varieties      192—193
Riesz potentials      117—121 130 133
Riesz transforms      57 65 75 78—79 112 125 136 143 213 242
Rotations      56 79
Singular integral operators      26—53 66 80 83 232 254
Sobolov spaces, $L^{p}_{k}$       122 135 159—160 180
Sobolov's theorem      124
Special Lipschitz domain      181 249
Spherical harmonics      68 71 73
Splitting of functions      246 267
Strict definition of a function      192
Symbol      80
vector-valued functions      45
Weak-type estimates      6 20 29—33 42 115 120 272
Young's inequality      271

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