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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

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Предметный указатель

$A_{\infty}$ condition      83
$\mathcal{F}_{\alpha, p}$ -thin set      183
( $\alpha$ , p)-capacities, relations between      129 148 151 153
( $\alpha$ , p)-capacity      VI 19 20 29 44 153 see
( $\alpha$ , p)-capacity and coverings      145
( $\alpha$ , p)-capacity and Hausdorff content      152
( $\alpha$ , p)-capacity and Hausdorff measure      129 151
( $\alpha$ , p)-capacity of ball      131
( $\alpha$ , p)-capacity of Cantor set      143 144
( $\alpha$ , p)-capacity of manifold      139
( $\alpha$ , p)-capacity, history      49
( $\alpha$ , p)-capacity, lower estimate in terms of Hausdorff content      137 139
( $\alpha$ , p)-capacity, quasiadditivity of      150
( $\alpha$ , p)-capacity, sharpness of comparison      146 147
( $\alpha$ , p)-capacity, under contraction      152
( $\alpha$ , p)-capacity, under Lipschitz mapping      140 141
( $\alpha$ , p)-capacity, upper estimate in terms of Hausdorff content      134
( $\alpha$ , p)-fine      176 see
( $\alpha$ , p)-fine topologies, comparison of      184
( $\alpha$ , p)-fine topology      186 see
( $\alpha$ , p)-quasicontinuity      156 see
( $\alpha$ , p)-quasicontinuous representative      156 158 159 see
( $\alpha$ , p)-quasieverywhere, ( $\alpha$ , p)-q.e.      20 see
( $\alpha$ , p)-thick set      see "Thick set"
( $\alpha$ , p)-thin set      see "Thin set"
Abel, N.H.      303
Absolute continuity on lines      238
Adams, D.R.      50 51 79—82 105 126 150—153 180 182—186 210—212 214 231 280
Adams, R.A.      7 14 155 231
Adjoint operator      47 319
Ahlfors modifier      280 324
Ahlfors, L.V.      49 280 327
Aikawa, H.      150 153
Aissaoui, N.      49
Analytic capacity      311 324 326
Analytic q-capacity      311
Analytic set      see "Suslin set"
Ancona, A.      82
Anger, B.      211
Annihilator      306
Annihilator of $D^{q}(E)$       313
Annihilator of $L^{q}_{a}(G)$       306 308 326
Annihilator of $L^{q}_{\mathcal{L}}(G)$       319
Annihilator of $R^{q}(E)$       309
Annihilator of $W^{m, p}_{0}(K^{c})$       235
Approximation by analytic functions in $L^{q}$       305 316
Approximation by analytic functions in $L^{q}$ and (1, p)-stability      310
Approximation by harmonic functions      279
Approximation by harmonic functions in $L^{q}$       305 318
Approximation by harmonic functions in $L^{q}$ and (2, p)-stability      322
Approximation by harmonic functions in $W^{1, q}$       316
Approximation by harmonic functions in $W^{1, q}$ and (1, p)-stability      312 313
Approximation by harmonic functions, uniform      326
Approximation by potentials in $L^{q}$       309
Approximation by potentials in $W^{1, q}$       314
Approximation by rational functions      305
Approximation by rational functions in $L^{1}$       324
Approximation by rational functions in $L^{q}$       309
Approximation by rational functions, constructive      325
Approximation by rational functions, uniform      311 324—326
Approximation by solutions of elliptic equations      318
Approximation by solutions of elliptic equations and bounded point evaluations      325
Approximation by solutions of elliptic equations in $L^{q}$ and ( $\alpha$ , p)-stability      322
Approximation of $C^{m}$ -functions vanishing on a set      233
Approximation of functions with vanishing trace      233 234 242 281 302
Approximation of nonnegative functions in $W^{m, p}_{0}(\Omega)$       235
Approximation, local degree of      85 122
Approximation, Sobolev problem      278
Area of (N — 1)-dimensional unit sphere      8
Aronszajn, N.      10—13 49 152 153 185
Arzela — Ascoli theorem      197
atom      VII 123 127
Atom, $C^{S}$ -      111
Atom, smooth      85 126 281 282
Atomic nonlinear potential      119—121 186
Atomic nonlinear potential and Wolff potential      119 121
Atomic nonlinear potential theory      127
Atomic potential      117
Atomic representation      85 111 113 187 281 282 296
Atomic representation and quasicontinuity      283
Babuska, I.      327
Bagby, T.      8 185 211 279 303 325—327
Balayage      184 308
Baras, P.      51
Bauman, P.      182
Beckner, W.      82
Benkirane, A.      49 82
Berger, M.      214
Bers, L.      280 324 326
Besicovitch, A.      153
Besov capacities, relations between      152
Besov capacity      105 167
Besov capacity and Hausdorff content      152
Besov capacity, dual definition      106 107 118
Besov nonlinear potential      106 107 126 167 168
Besov space      VI 80 85 86 125 155 302
Besov space, atomic representation      111 113
Besov space, equivalent norm      87 89 111 113
Besov space, homogeneous      86
Besov space, potential representation      105
Besov space, representation theorem      90 104
Besov space, weighted      97
Besov, O.V.      125
Bessel capacity      38 131
Bessel capacity, compared to Riesz capacity      131 150
Bessel function      11
Bessel kernel      9 50 193 198
Bessel kernel as elementary function      12
Bessel kernel, analyticity of      11
Bessel kernel, asymptotic formulas      11 12
Bessel kernel, compared to Riesz kernel      10
Bessel kernel, derivative of      13
Bessel kernel, group property      10 21
Bessel kernel, integral representation      10
Bessel kernel, Laplace transform representation      12
Bessel kernel, positivity      10
Bessel kernel, representation by Bessel function      11
Bessel potential      10
Bessel potential space      VI 13
Bessel potential space as Lizorkin — Triebel space      92 204 281
Bessel potential space, dual of      13
Bessel potential space, equivalent norm on      122
Bessel potential, derivatives      57
Bessel potential, integral estimate      56
Bessel potential, name of      11
Bessel potential, nonlinear      38
Bessel potential, representation as      20
Beurling, A.      V 49 50 81 82 153 279 327
BMO, functions of bounded mean oscillation      79 92 126
Boccardo, L.      82
Bochner, S.      11
Borel property of $e_{\alpha, p}(E)$       174
Borel sets, capacitability of      28
Borichev, A.A.      150
Boundary regularity      165 166 181—183
Boundary regularity, modulus of continuity      182
Boundary values      129 142 153 161 181
Bounded mean oscillation      79 92 126
Bounded point evaluation      325
Bounded variation      181
Boundedness principle      39 40 50 190 214 264
Bourdaud, G.      80
Branson, Th.P.      81
Brelot, M.      150 152 185 186 278
Brennan, J.E.      326
Brezis, H.      67 82 238 280
Browder, F.E.      67 82 238 280
Brownian motion      48
Burenkov, V.L      279
BV, functions of bounded variation      181

Caffarelli, L.      50
Calderon Extension Theorem      7 142 238
Calderon theorem      13 20
Calderon — Zygmund theorem      6 94
Calderon, A.P.      6 7 10 13 238
Calderon, C.P.      185
Campanato space      79 151
Cantor set      129 143 147 149
Cantor set, ( $\alpha$ , p)-capacity of      143 144
Cantor set, Hausdorff measure of      143 153
Capacitability      42
Capacitability for Hausdorff content      138
Capacitability of Borel sets      28
Capacitability of Suslin sets      28
Capacitability theorem      28
Capacitable set      28
Capacitary function      21 28 35—37 106—108 119
Capacitary integral      212 230
Capacitary integral, sublinearity of      211
Capacitary measure      21 35 37 108 151 165 168 170 171 229 264
Capacitary measure, outer      37 168
Capacitary potential      21 28 174 264 312
Capacitary potential, boundedness of      41
Capacitary strong type inequality      181 187 189 199 200 209
Capacitary strong type inequality in Lizorkin — Triebel space      204
Capacitary strong type inequality, failure of      209
Capacitary strong type inequality, history of      213
Capacitary weak type inequality      188
Capacity      V 17 18
Capacity and algebraic properties of set      226
Capacity and Lebesgue measure      38 39
Capacity and stochastic processes      48 51
Capacity for ball      129
Capacity in spaces with mixed norm      107
Capacity, $L^{p}$ -, for general kernel      25 104
Capacity, $N_{\alpha, p}$       45
Capacity, ( $\alpha$ , p)-      VI 19 20 29 44 153 see p)-capacity"
Capacity, analytic      311 324 326
Capacity, analytic q-      311
Capacity, atomic      118
Capacity, Besov      104 105 162
Capacity, Bessel      38 131
Capacity, condenser      209 312
Capacity, distribution      45
Capacity, dual definition      21 34 35 106 107 118 220 311 326
Capacity, equivalence of $C_{\alpha, p}$ and C( $\cdot$ ; $F^{p, q}_{\alpha}$ )      107
Capacity, equivalent      20 65 105
Capacity, instability of      314 324 325
Capacity, Lizorkin — Triebel      104 105
Capacity, Lizorkin — Triebel, dual definition      107 118
Capacity, Lizorkin — Triebel, equivalence with ( $\alpha$ , p)-capacity      203
Capacity, maximizing property of      36
Capacity, Newton      17
Capacity, outer      19 25 153
Capacity, parabolic      214
Capacity, polynomial      226 322 327
Capacity, probabilistic interpretation of      48 51
Capacity, relative      223 241
Capacity, Riesz      38 131
Capacity, scale invariance of      167 224
Capacity, sets of zero      26 263 266 271
Capacity, strongly subadditive      211 212
Capacity, subadditivity of      26
Capacity, triviality of      38 189
Carleman, T.      325
Carleson, L.      VI 40 48—51 81 138 151—153 186 326 327
Carlsson, Anders      180 231 301
Cartan, H.      V 326
Cauchy — Riemann equation      306
Cauchy — Riemann operator      47 306
Cauchy, A.      11
Chain rule      62 239
Chandrasekharan, K.      89 91
Chang, S.-Y.A.      81 82
Characterization of $f \in L^{\alpha, p}_{0}(E)$       281 302
Characterization of $f \in W^{m, p}_{0}(\Omega)$       234
Choquet property      155 165 175 185
Choquet theorem      28 138
Choquet, G.      28 49 185 211 327
Cioranescu, D.      325
Clarkson inequalities      14
Clarkson theorem      14
Clarkson, J.A.      14
Classical potential theory      V VI 17 18 20 21 39 41 42 48 50 151—153 155 164 184—186 308
Closure of $\Omega_{E}$ description of      27
Cohn, W.S.      126
Coifman, R.      83
Coincidence of positive cones      103 126
Compact imbedding      227
Compactness of imbedding      187 195 198
Comparison theorem      134 137 139
Complex interpolation      29
Condenser capacity      209 312
Conformal invariance      49
Connectedness in fine (quasi-) topology      184
Connectedness, arcwise      184
Connectedness, local      184
Continuity of imbedding      187 191 193 210
Continuity of restriction to subspace      142
Continuity principle      41 50
Contraction      62 82 152
Convex set, weak closure of      15
Convolution      4
Convolution, maximal function estimate of      102
Covering lemma, Maz'ya — Preobrazhenskii      211
Covering lemma, Netrusov      302
Covering lemma, simple Vitali      16
Covering lemma, Whitney      16 see
Dahlberg, B.E.J.      80 82 83 213
Dal Maso, G.      182 325
Daubechies, I.      127
Davie, A.M.      184
Davis, Burgess      184
de la Vallee Poussin, Ch.-J.      V
Degree of approximation, local      85 122
Dellacherie, C.      49
Deny, J.      V 7 10 50 82 153 185 186 278 279 307 308 326
Derivative of potential      57 259
Derivative of product      158 241
Diestel, J.      15
Differentiability      164 303
Differentiability, fine      184
Differential and zero trace      287
Differential of order s      282 283 293 299 323
Dirac distribution, measure      8 228
Dirac distribution, measure, sweeping of      308
Dirichlet integral      327
Dirichlet principle      V
Dirichlet problem      V VIII 164 165 181—183
Dirichlet problem and (1, 2)-stability      312
Dirichlet problem for p-Laplace equation      166
Dirichlet problem for polyharmonic equation      183 236 237 278
Dirichlet problem in domains with many holes      325
Dirichlet problem, fine      278
Dirichlet space      82 279
Distinguished element      155
Distinguished representative      187
distribution      V 4
Distribution in $W^{-m, p^{'}}$ , approximation of      235
Distribution in $W^{-m, p^{'}}$ , nullspace of      235
Distribution of order m, nullspace of      233
Distribution, capacity      45
Distribution, positive      4 22
Distribution, temperate (tempered)      4
Divergence of positive series      288 303
Donchev, T.      183
Doob, J.L.      VII 48 185
du Plessis, N.      48
Dual approximation problem      306
Dual definition of $N_{\alpha, p}(K)$       45

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