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Adams R.A. — Sobolev Spaces
Adams R.A. — Sobolev Spaces

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Название: Sobolev Spaces

Автор: Adams R.A.

Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1975

Количество страниц: 268

Добавлена в каталог: 08.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^m$-regularity      67
$\Delta$-regular      232
$\Delta_2$-condition      231 232
$\lambda$-fat cube      161
$\sigma$-algebra      13
$\varepsilon$-net      7
Almost everywhere      14
Approximation theorem      14
Approximation theorem for Lebesgue spaces      28 31
Approximation theorem for Orlicz spaces      240
Approximation theorem for Orlicz — Sobolev spaces      247
Approximation theorem for Sobolev spaces      52 54 57 205 207
Aronszajn, N.      219
Ascoli — Arzela theorem      10
Banach algebra      115
Banach space      4
Besov space      177 223
Besov, O.V.      218 223
Bessel potential      219 220
Bochner integral      178
Boundary      2
Bounded operator      9
Browder, F.E.      70 79
Caiderdn, A.P.      83 89 91 219 221
Caldcron — Zygmund inequality      91
Calder6n extension theorem      91
Capacity      152
Cartesian product      8
Cauchy sequence      4
Characteristic function      14
Clark, C.W.      175
Clarkson’s inequalities      37
Compact imbedding      9
Compact imbedding theorem for continuous function spaces      11
Compact imbedding theorem for Orlicz — Sobolev spaces      249 252 256 259
Compact imbedding theorem for Sobolev spaces      144 151 157 162 163 166 167 170
Compact set      6
Compact support      2
Complementary N-function      229
Complete orthonormal system      173
Completeness      4
Completeness of Lebesgue spaces      26
Completeness of Orlicz spaces      234
Completeness of Orlicz — Sobolev spaces      246
Completeness of Sobolev spaces      45
Completion      4
Complex interpolation method      177 221
Cone      65 96
Cone property      66
Cone property, uniform      66
Cone, standard      124
Conjugate exponent      23
Conjugate N-function      248
Continuous functional      3
Convergence in the sense of $\mathcal{D}(\Omega)$      19
Convergence, norm      4
Convergence, weak      6
Convexity, local      3
Convexity, uniform      7 34 46
Convolution      29 90 199
Countably additive      13
Cusp      122 123
Cusp, exponential      122
Cusp, standard      124
Cylindrical coordinates      124
Dense      4
Derivative of a distribution      20
Derivative, distributional      21 179
Derivative, weak      21
distribution      19
Distribution, tempered      220
Distributional derivative      21 179
Domain      1
Dominated Convergence Theorem      17
Dominating N-function      231
Donaldson, T.K.      247
Dual space      3
Dual space of a Lebesgue space      40 41
Dual space of a Sobolev space      48—51
Dual space of an Orlicz space      238
Dual space of an Orlicz — Sobolev space      247
Ehrling, C      70 75 79
Embedding      see “Imbedding”
Equivalent N-function      231
Equivalent norm      4 8
Equivalent norm for Sobolev spaces      79 158 214 223
Essential rate of increase      231
Essential supremum      24
Essentially bounded      24
Extension operator      83
Extension theorem      84 88 91 211
Fatou’s Lemma      17
Finite cone      65
Finite width      158
Flow      169
Fourier transform      220
Fractional order spaces      177
Fractional order spaces, Besov spaces      223
Fractional order spaces, Nikoskii spaces      225
Fractional order spaces, Sobolev spaces      204 206
Fractional order spaces, spaces of Bessel potentials      219 221
fringe      161 165
Fubini’s Theorem      18
Functional      3
Gagliardo, E.      67 68 70 75 95 99 101
Hahn — Banach extension theorem      6
Hestenes, M.      83
Hilbert space      5
Hilbert — Schmidt imbedding      175 176
Hilbert — Schmidt operator      174
Holder condition      10
Holder’s Inequality      23 234
Holder’s inequality, reverse form      24
Homogeneous function      91
Imbedding      9 96
Imbedding constant      97
Imbedding inequality, weighted norms      128 133 136 138
Imbedding theorem for Besov and Nikorskii spaces      224—226
Imbedding theorem for continuous function spaces      11
Imbedding theorem for cusp domains      126 127
Imbedding theorem for Lebesgue spaces      25
Imbedding theorem for Orlicz spaces      234 237
Imbedding theorem for Orlicz — Sobolev spaces      249 252 255 256 259
Imbedding theorem for Sobolev space $W^{m,p}$      97 242
Imbedding theorem for Sobolev space $W^{s,p}$      216—219
Imbedding theorem, direct and converse      217—219
Imbedding, compact      9 (see also “Compact imbedding”)
Imbedding, compact, theorem, Hilbert — Schmidt      175 176
Imbedding, compact, theorem, trace      96
Infinitesimal generator      181
Inner product      5
Integrability, Bochner      179
Integrability, Lebesgue      15 17
Integrability, local      19 179
Integral, Bochner      178 179
Integral, Lebesgue      15 17
Interpolation inequality      70 74 75 78 79 81 82
Interpolation method, complex      177 221
Interpolation method, real      177
Interpolation method, trace      178 186
Interpolation space      188
Interpolation theorem between Banach spaces      188 222
Interpolation theorem between spaces $L^{s,p}$      222
Interpolation theorem between spaces $W^{m,p}$      74 75 78 79
Interpolation theorem involving compact subdomains      81 82
Isometric isomorphism      4
Kernel      204 214—218
Kondrachov, V.L      143
Kondrachov, V.L, Rellich — Kondrachov theorem      144
Lebesgue dominated convergence theorem      17
Lebesgue integral      15 17
Lebesgue measure      13 14
Lebesgue spaces      22 24
Leibniz formula      2 21
Lichenstein, L.      83
Linear functional      3
Lions, J.L.      56 178 184 219
Lipschitz property      66
Lizorkin, P.I.      218
Local integrability      19 179
Localization theorem      207
Locally convex TVS      3
Locally finite      65
Lusin’s theorem      14
Luxemburg norm      234 253
m-Smooth transformation      63
Magenes, E.      178 219
Maurin, K.      174
Measurable function      14 17 178
Measurable set      13
Measure      13
Measure, complex      13
Measure, Lebesgue      14
Measure, positive      13
Meyers, N.      45 52
Minkowski’s inequality      23
Minkowski’s inequality, reverse form      24—25
Mollifier      29
Monotone Convergence Theorem      16
Morrey, C.B.      95 98
Multi-index      1
N-function      227 228
Nikollskii, S.M.      177 225 226
Nirenberg, L.      70 75
Norm      3
Norm, equivalence      4 8 79 158 214 223
Normable space      4
Normed dual      5
Normed space      4
Operator      8
Operator, bounded      9
Operator, compact      8
Operator, completely continuous      9
Operator, extension      83
Operator, imbedding      9
Orlicz class      232
Orlicz space      227 233 236
Orlicz — Sobolev space      246—247
Orthonormal system      173
Parallelepiped      65
Parallelogram law      5
Partition of unity      51
Polar set      56
Precompact set      7 31 33 242
Product, cartesian      8
Product, inner      5
Quasibounded domain      148
Quasicylindrical domain      159
Radon — Nikodym theorem      17
Reflexivity      6
Reflexivity of Lebesgue spaces      42
Reflexivity of Orlicz spaces      240
Reflexivity of Orlicz — Sobolev spaces      247
Reflexivity of Sobolev spaces      47 205
Reflexivity of trace interpolation spaces      189—190
Regularization      29
Rellich — Kondrachov theorem      144
Rellich, F.      143
Riesz representation theorem for Hilbert space      5
Riesz representation theorem for Lebesgue spaces      40 41
Scale of spaces      188
Schwartz distribution      18 19
Second dual      6
Seeley, R.      83 86
Segment property      54 66
Semigroup of operators      180
Separability      4
Separability of Lebesgue spaces      28
Separability of Orlicz spaces      240
Separability of Orlicz — Sobolev spaces      247
Separability of Sobolev spaces      47
Serrin, J.      45 52
Simple extension operator      83 91
Simple function      14 178
Smith, K.T.      219
Sobolev conjugate N-function      248
Sobolev imbedding theorem      95 97
Sobolev imbedding theorem, limiting case      242
Sobolev inequality      104
Sobolev space      44
Sobolev space, equivalent definitions      52
Sobolev space, fractional order      177 204 205 206
Sobolev space, integral order      44
Sobolev space, negative order      50 51
Sobolev, S.L.      45 95
Spherical coordinates      130
Spiny urchin      151—152
Stone — Weierstrass theorem      10
streamline      169
Strong extension operator      83 84
Strong local Lipschitz property      66
subspace      5
Support      2
Tempered distribution      220
Tesselation      106 161
Testing function      19
Topological vector space (TVS)      2
Total extension operator      83 88
Trace      96 185 186
Trace on a subspace      96 112
Trace on the boundary      113 114 215—217
Trace, higher-order      196 198
Trace, interpolation method      178 186
Trace, interpolation space      186 198
Transformation of coordinates      63—64
Trudinger, N.S.      228 242 247
Uniform $C^m$-regularity      67
Uniform cone property      66
Uniform convexity      7
Uniform convexity of Lebesgue spaces      34 38
Uniform convexity of Sobolev spaces      47
Uspenskii, S.V.      218
Vector sum of Banach spaces      184
Volume      14
Weak convergence      6
Weak derivative      21
Weak sequential compactness      7
Weak topology      6
Weak-star topology      3 19
Young’s function      227 253
Young’s inequality      230
Young’s theorem      90
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