Adams D.R., Hedberg L.I. — Function spaces and potential theory :: Электронная библиотека попечительского совета мехмата МГУ

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Adams D.R., Hedberg L.I. — Function spaces and potential theory

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Название: Function spaces and potential theory

Авторы: Adams D.R., Hedberg L.I.

Аннотация:

Proceedings of the Edinburgh Mathematical Society

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 382

Добавлена в каталог: 21.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Mergelyan, S.N.      326
Meyer, P.-A.      49
Meyer, Y.      80 127
Meyers, N.G.      VI 7 49 50 79 127 152 153 183 185 186 231 280 323
Michael, J.H.      181
Mikhlin — Hoermander multiplier theorem      93 125 126
Mikhlin, S.G.      85 93 126
Minimax theorem      30 34 49 50
Minimizing sequence, convergence of      15
Minkowski inequality      4
Minty, G.J.      140
Mixed norm      3 78 86 104 117
Mizuta, Y.      184
Modified Bessel function of the third kind      11
Module, closed $C^{\infty}_{0}$ -      293—295
Modulus of continuity      182
Modulus of curve family      49
Molchanov, A.M.      231
Monotone norm      202
Morawetz, C.      15
Morrey — Campanato space      79 151 214
Morrey, C.B., Jr.      7
Morris, G.R.      81
Mosco, U.      182
Moser inequality      81
Moser, J.      81
Muckenhoupt $A_{\infty}$ condition      83
Muckenhoupt — Wheeden theorem      72 83 103 107 126 214
Muckenhoupt, B.      53 83
Mulla, F.      12 13 49
Multiindex      2
Multiindex, length of      2
Multiplier      66 67 241 281 282
Multiplier theorem of Marcinkiewicz      126
Multiplier theorem of Mikhlin — Hoermander      93 125 126
Multiplier, construction of      242 243 247 291
Multiresolution analysis      127
Murat, F.      82 325
Nagel, A.      181
Netrusov, Yu.V.      VII VIII 126 127 150 152 153 164 181 209 211—214 233 281 294 301—303 327
Newton capacity      17
Newton kernel      8
Newton potential      8 17
Nieminen, E.      211
Nikol'skii, S.M.      88 125
Nilsson, Per      126
Nirenberg, L.      79
Non-increasing rearrangement      60
Nonlinear potential      VI 21 36 46 49 166 167 169 175 183 186
Nonlinear potential theory      VI VIII 18 48 49 85 233
Nonlinear potential theory, atomic      85 127
Nonlinear potential, atomic      119—121 186
Nonlinear potential, Besov      106 107 126 167 168
Nonlinear potential, Bessel      38
Nonlinear potential, estimate of derivatives      259
Nonlinear potential, Harnack property      257 259 262
Nonlinear potential, Lizorkin — Triebel      108
Nonlinear potential, lower estimate      44 45 257 258
Nonlinear potential, Riesz      38
Nonlinear potential, smooth truncation of      262 264 272
Nontangential limit      161
Nonvanishing condition      89 102
Norm on space of quasicontinuous functions      199
Norm, monotone      202
Nystroem, K.      226 327
O'Neil lemma      60
O'Neil, R.      61 81
Obstacle problem      50 182
Ohtsuka, M.      153
Oksendal, B.      184
Olivier, L.      303
One-sided approximation      66 82 238
One-sided approximation in Orlicz — Sobolev spaces      82
One-sided approximation, parabolic      82
Operator, $\mathcal{D}^{\alpha}$       68 83
Operator, $\mathcal{D}^{\alpha}$ , pointwise estimate of      69
Operator, $\mathcal{E}^{\alpha}$       122
Operator, $\mathcal{S}^{\alpha}$       72 83 122
Orlicz — Sobolev spaces      82
Orobitg, J.      302 303 325
Outer capacity      19 25 153
p-Laplace equation      VIII 166 182
p-Laplace operator      VIII 20
p-superharmonic function      182
Pairing      4
Parabolic equation      182
Parabolic potential      214
Parseval formula      5
Partial differential equation, boundary regularity      165 166 181—183 see
Partial differential equation, elliptic      see "Elliptic equation"
Partial differential equation, linear second order      20
Partial differential equation, nonlinear      VI 20 67 82
Partial differential equation, parabolic      182
Partial differential equation, quasilinear      VIII 48 51 166 182 183
Partial differential equation, removable singularity      see "Removable set"
Partition of unity      86
Peetre maximal function      97
Peetre theorem      87 97
Peetre, J.      85 87 89 97 125 126
Perez, C.      83 126
Perron method      48
Phong, D.H.      210
Pierre, M.      51
Pisarevskii, B.M.      324 327
Plancherel theorem      5
Poincare inequality      8 215 231
Poincare type inequality      215 238
Poincare type inequality and closed graph theorem      226
Poincare type inequality and thickness      245 267
Poincare type inequality, depending on capacity      225 226 241
Poincare type inequality, depending on capacity, best constant in      231
Point of absolute convergence      283 287
Pointwise bounded approximation      66 238
Pointwise estimate of potential      54 55
Poisson integral      161 181
Poisson, S.      11
Polar set      59
Polishchuk, E.M.      303
Polking, J.C.      50 51 82 83 279 325 327
Polynomial approximation of functions vanishing on a set      223 229
Polynomial approximation, local      122
Polynomial capacity      226 322 327
Pompeiu formula      307
Porous set      212
Positive cone in $B^{p, q}_{-\alpha}$       90 110 126
Positive cone in $F^{p, q}_{-\alpha}$       102 103 110 126
Positive cone in $L^{-\alpha, p}$       103 110 126
Positive cone in $L^{p}(E)$       2
Positive cone in $\mathcal{M}(\Omega)$       2
Positive cone of distributions      4
Positive cone, coincidence of      103 126
Positive distribution      4
Potential      24
Potential and fractional maximal function      72 75 78
Potential, atomic      117
Potential, average of      43
Potential, compared to sum      77 28
Potential, continuity of      41 42
Potential, equilibrium      17
Potential, Newton      8 17
Potential, parabolic (heat)      214
Preobrazhenskii, S.P.      211
Principal value integral      5
Product rule      158 241
Projection      V 227 228
Quasi-Lindeloef property      184
Quasiadditivity of ( $\alpha$ , p)-capacity      150
Quasiclosed      178
Quasiconformal mapping      49
Quasicontinuity      155 156 179 186 317

Quasicontinuity and atomic representation      283
Quasicontinuity and fine continuity      177 178
Quasicontinuity and Hausdorff content      180 181
Quasicontinuity of Besov potential      168
Quasicontinuity, Hoelder type      181
Quasicontinuous function, integrability of      187 188 212 227
Quasicontinuous function, measurability of      187 188
Quasicontinuous functions, space of      200
Quasicontinuous representative      156 158 159 180 181 185 219 234 281
Quasicontinuous representative, integrability of      187 188 212 227
Quasicontinuous representative, uniqueness of      157 158 178 185
Quasieverywhere      20
Quasieverywhere, (g, p)-      26
Quasilinear equation      VIII 48 51 166 182 183
Quasiopen      178 317
Quasitopology      178
Quasitopology, connectedness in      184
Rademacher functions      92 95
Radon measure      2
Regular point      164 181
Regular point, Wiener criterion for      165 166 see
Relative capacity      167 223 241
Removable set      47 51 65 306 326 327
Removable set for $W^{m, p}$       237 278
Representation formula      308
Representation formula for functions vanishing on a set      219 222
Representation formula, Sobolev      217
Reshetnyak, Yu.G.      VI 49 152 153
Rickman, S.      182
Riemann Theorem      51
Riemannian manifold      82
Riesz capacity      38 131 see
Riesz kernel      9 193 198
Riesz kernel, integral representation      10
Riesz kernel, modified      74 223
Riesz kernel, singular      5
Riesz potential      9
Riesz potential space      13
Riesz potential, derivatives of      57
Riesz potential, integral estimate of      56
Riesz potential, nonlinear      38
Riesz potential, pointwise estimate of      54 55
Riesz potential, weak type estimate of      56
Riesz transform      5
Riesz, M.      V 5
Riviere, N.M.      185
Rogers, C.A.      138 152
Rubio de Francia, J.L.      83
Rudin, W.      VI 2 5 14—16 25 140 181 197 208 303 305 307 312
Runge theorem      305
Saak, E.M.      322
Sawyer, E.T.      83 153 210 214
Schechter, M.      214
Schroedinger operator      213
Schulze, B.-W.      279 327
Schwartz class      4 85
Schwartz distribution      4
Schwartz, L.      V 2 4 5 12 50 158 279 306 319
Segala, F.      182
Segment property      278
Semicontinuity      3 24 121
Seminorm, null space of      227
Sequence space      116 117
Serrin, J.      VI 7 48 49 51 153
Set of capacity zero      26 263 266 271
Set of infinities of potential      26 49 153
Set of non-uniqueness for $L^{\alpha, p}$       314
Set of uniqueness for $L^{\alpha, p}$       314
Set, analytic      see "Suslin set"
Set, porous      212
Shapiro, Harold S.      125
Shapiro, Joel H.      181
Shaposhnikova, T.O.      212 213 303
Sharp exponential estimate      58 81 82
Sharp inequality      81
Simple Vitali lemma      16
Sinanyan, S.O.      326
Singular integral operator      6
Singular Riesz kernel      5
Singularity, removable      see "Removable set"
Sion, M.      49
Sjoedin, T.      49 126 185
Skrypnik, I.V.      183
Smith, K.T.      10—13 49 152 153 185
Smooth atom      see "Atom"
Smooth truncation      63 80 150 209 213 240
Smooth truncation of non-negative functions      80
Sobolev algebras      303
Sobolev imbedding theorem      14 56 80 155
Sobolev inequality      81 218
Sobolev representation formula      215 217
Sobolev space      V—VIII 6 233
Sobolev space, homogeneous version      8
Sobolev space, pointwise representation      8 215 217
Sobolev space, potential representation      9 10 13 20
Sobolev space, weighted      185
Sobolev trace theorem      236 278
Sobolev uniqueness theorem      237 278
Sobolev, S.L.      7 14 81 155 231 236 237 278
Space of quasicontinuous functions      200
Space of quasicontinuous functions, minimality of      202
Spectral measure      50
Spectral synthesis      279
Spectral synthesis, 2m-      279
Spectral synthesis, counterexamples      279
Spectrum      279
Spherical h-density      151
Stability      205
Stability and approximation by harmonic functions      312
Stability and approximation in $L^{q}_{a}$       310
Stability and Dirichlet problem      312
Stability and thickness      320
Stability of nowhere dense set      314
Stability, definition of ( $\alpha$ , p)-      319
Stability, necessary and sufficient condition for ( $\alpha$ , p)-      320 322
Stability, necessary condition for ( $\alpha$ , p)-      220
Stability, sufficient condition for ( $\alpha$ , p)-      320
Stable set      309 313 314 316 319 320 322
Stable set, example of non-      314 321
Stampacchia, G.      79 82 181 182 279
Stein, E.M.      VI 3—11 13 14 16 56 83 92 125 126 159 161 185 189 192 238 263 265 315
Stochastic processes      48 51
Strichartz theorem      72 85 122 127
Strichartz, R.S.      81 83 127 208
Stromberg, K.      14
Strong subadditivity      211 212
Strong type inequality      see "Capacitary strong type inequality"
Subadditivity of capacity      26
Subadditivity of capacity, strong      211 212
Submodule of $L^{\alpha, p}$       293 294
Suslin set      35 49 170
Suslin set, capacitability of      28 29
Suslin, M.Ya.      50
Sweeping      184 308
Szeptycki, P.      12 13 49
Tarkhanov, N.N.      51 325 326
Tauberian condition      89 102
Taylor formula      215 220
Taylor polynomial      2 228 282 283
Taylor polynomial as ring homomorphism      293
Taylor, S.J.      151—153
Temperate (tempered) distribution      4
Test function      4
Thick set      164 166 241 266 320
Thick set, uniformly      242 243
Thickness and Poincare type inequality      245
Thickness and zero trace      246
Thin set      155 164—166 182 183 186 241 316
Thin set, $\mathcal{F}_{\alpha, p}$ -      183
Thin set, Brelot characterization of      155 165 168 185 186

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