Aikawa H., Essen M. - Potential Theory - Selected Topics :: Электронная библиотека попечительского совета мехмата МГУ

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Название: Potential Theory - Selected Topics

Авторы: Aikawa H., Essen M.

Аннотация:

The first part of these lecture notes is an introduction to potential theory to prepare the reader for later parts, which can be used as the basis for a series of advanced lectures/seminars on potential theory/harmonic analysis. Topics covered in the book include minimal thinness, quasiadditivity of capacity, applications of singular integrals to potential theory, L(p)-capacity theory, fine limits of the Nagel-Stein boundary limit theorem and integrability of superharmonic functions. The notes are written for an audience familiar with the theory of integration, distributions and basic functional analysis.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 212

Добавлена в каталог: 01.06.2008

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

Предметный указатель

$(K_y)_{\mathcal{E}}$       191
condition      151
$b^E_{\mathcal{E}_x}$       185
$b^E_{\mu}$       185
$B_{\alpha,p}$       132
$c*_{k,P}(A)$       115
$C_0(\mathbb{R}^n)$       107
      176
      153 155
      176
$C_{k,p}$ -a.e.      110
$C_{k,p}$ -capacitary distribution      118
$C_{k,p}$ -capacitary potential      118
$C_{k,p}(A)$       109
$C_{\bar{k},p}$ -capacitary distribution      112
      176
      161
      149
$G^{1,\alpha}$ -domain      157
      155
      176
      185
$g_{\alpha}$       132
$G_{\delta}$ -set      121
$H_{h,R}(E)$       130
$H_{h}(E)$       130
$h_{\mathcal{E}}$       190
      159
      158
$k(x,\mu)$       107
$k(\mu,\nu)$       109
$k(\nu,y)$       109
      174
      157
$k_{\alpha}$       132 145
$K_{\sigma\delta}$       182
$K_{\sigma}$ -set      121
-integrability      179
-norm      108
$L^p(\mathbb{R}^n)$       109
$L^{p'}(\mathbb{R}^n)$       108
$M_{k,R\mu}$       133
$M_{k\mu}$       126
$M_{\alpha}f$       149
$m_{\beta}$       145
$PI(\mu)$       163
solution      190
      173 175
$p_{\Omega}$       174
      153
      153
      155
$R_{\alpha,p}$       132 145
      153
      153
$u_{\mu}$       137
$V^{\nu}_{k,p}$       120
$W^{\mu}_k$       132
$W^{\mu}_{k,q}$       132
      158 185
      153
$\alpha$ -thin      155
$\alpha-n(\psi)$       172
$\approx$       123
$\bar{E}^{mf}$       188
$\bar{k}$       123
$\bar{\mathcal{D}}_{f,h}$       190
$\bar{\Omega}$       185
$\Delta$       158 185
$\delta(x)$       145
$\Delta_0$       159 185
$\delta_1$       158 185
$\gamma(E)$       159
$\Gamma(X, a, t)$       171
$\Gamma_e$       173
$\gamma_g(E)$       155
$\Gamma_i$       172
$\gamma_u(E)$       153
$\hat{f}$       106
$\hat{R}_u^K$       153
$\hat{\Omega}$       158
$\Lambda(E)$       161
$\lambda_{\Omega}$       175
$\mathcal{D}_{f,h}$       190
$\mathcal{E}_E$       188
$\mathcal{E}_x$       185
$\mathcal{L}_{f,h}$       190
$\mathcal{M}f$       124
$\mathcal{M}_{ap}f$       149
$\mathcal{M}_{\mu}$       124
$\mathcal{M}_{\mu}(X,r)$       163
$\mathcal{U}_{f,h}$       190
$\mathfrak{M}^1_A$       117
$\mathfrak{M}^t_K$       116
$\mu_h$       159 185
$\mu_u$       185
$\mu_{X,r,t}$       167
$\nu^x_h$       190
$\omega$       160
$\Omega$ -fine      171
$\Omega$ -near fine      171
$\Omega(y)$       160
$\Omega+X$       160
$\omega^x_h$       190
$\Sigma$       147
$\Sigma_n$       176
$\sigma_u$       153
$\tilde{E}$       156
$\underline{\mathcal{D}}_{f,h}$       190
$\|f\|_p$       108
$\|f\|_{q,\beta}$       150
(NS)      160
(X, y)      159
A      123
Analytic set      112 114 182
Balayage      185
Banach - Saks theorem      111
Bessel kernels      132
BMO      174
Borel set      183
Boundary Harnack principle      180
Bounded curvature      171
c.s.a.      109
Calderon - Zygmund lemma      151
cap(E)      153
Capacitable      112 182
Capacitary distribution      112
Capacitary measure      120
Capacitary potential      120
Capacity strong type inequality      140
Carleson type measure      140
Choquet capacity      182

Choquet's capacitability theorem      112
Clarkson's inequalities      113
Classical capacity      123
Coarea formula      175
Comparable measure      147 149
Concentrated      114
Cone condition      160
Constant of comparison      123
Contraction mapping      133
Countably subadditive      109 114
Covering lemma      163
Cross section condition      160
d(F)      145
Dirichlet integral      153
Doubling condition      124
Doubling function      177
Duality      115 149
Essential projection      169
esslim      169
Exponential integrability      174
Extended minimum principle      189
Exterior ball      171
F*      106
Fatou - Naim - Doob theorem      158
Fefferman - Stein #-maximal function      150
Fractional maximal function      149
G(x, y)      158 185
Gegenbauer function      179
Gegenbauer polynomial      179
Global integrability      171
Good $\lambda$ inequality      126
Green capacity      153 155
Green energy      152
Green formula      176
Green function      158 176 185
h-harmonic measure      190
h-resolutive      190
Hahn - Banach theorem      136
Hardy's inequality      154
Harmonic measure      152 172 180 185
Harnack property      147 153
Hausdorff dimension      145
Hausdorff measure      130
Hausdorff type outer measure      161
Holder domain      174
Inner capacity      114
Inside barrier      172
Interior $\theta$ -wedge condition      175
Interior ball      171
Jensen's Inequality      139
K(x, y)      157 158 185
k(x,f)      109
k-Lipschitz domain      172
Kerman - Sawyer inequality      126
l(L)      181
l.s.c      105
Liapunov domain      157
Lie eventually outside      162
Lipschitz domain      157 159 172
Lipschitz mapping      132
Local integrability      171
Logarithmic capacity      153
Lower regularization      106 185
Lower semicontinuous      105
Lusin theorem      165
Martin boundary      158 185
Martin compactification      158 185
Martin kernel      157 185
Martin representation theorem      159 185
Maximal function      149
Maximal order of barrier      172
Mazur theorem      111
Mean value theorem      140
Measure function      130
mf lim      159 189
mfliminf      189
mflimsup      189
Mini-max theorem      115
Minimal      158
Minimal fine closure      188
Minimal fine limit      159
Minimal fine limit theorem      158
Minimally thin      157 159 187
Minkowski inequality in the integral form      172
Monotone      109 114
Naim $\Theta$ kernel      153
Nearly thin      171
Newtonian capacity      153
Nonlinear potential      120 137
Nontangential limit      170
Norm estimate      149
nt lim      169
NTA domain      157 159
Outer capacity      109 115
P      159
p-Laplace equation      174
Poincare metric      175
Poisson integral      163
PWB solution      185
Quasi-hyperbolic metric      174
Quasiadditivity      145
Quasidisjoint decomposition      147
Reciprocity      185
Refined Wiener criterion      155
Regularized reduced function      153 185
Riesz capacity      145
Riesz Decomposition theorem      159 185
Riesz kernel      132 145
Riesz - Martin representation theorem      185
Saddle point      118
Sard theorem      177
Separated sequence      156
Singular harmonic function      162 194
Thin      171
Thin at $\partial\Omega$ with respect to capacity      170
Thin at $\partial\Omega$ with respect to measure      161
Truncated maximal function      163
Truncated nontangential cone      171
Two-weight norm inequality      151
u.s.a      105
Uniformly $\Delta$ -regular      152 180
Universally capacitable      182
Universally measurable      114
Upper regularization      106
Upper semicontinuous      105
Vague convergence      107
Weak convergence      109
Weak maximum principle      137
Weak type estimate      163
Weighted integrability      179
Weighted norm inequality      151
Whitney decomposition      127 145 153 170
Wiener criterion      155 159

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