Murai T. — A Real Variable Method for the Cauchy Transform, and Analytic Capacity :: Электронная библиотека попечительского совета мехмата МГУ

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Murai T. — A Real Variable Method for the Cauchy Transform, and Analytic Capacity

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Название: A Real Variable Method for the Cauchy Transform, and Analytic Capacity

Автор: Murai T.

Аннотация:

This research monograph studies the Cauchy transform on curves with the object of formulating a precise estimate of analytic capacity. The note is divided into three chapters. The first chapter is a review of the Calderón commutator. In the second chapter, a real variable method for the Cauchy transform is given using only the rising sun lemma. The final and principal chapter uses the method of the second chapter to compare analytic capacity with integral-geometric quantities. The prerequisites for reading this book are basic knowledge of singular integrals and function theory. It addresses specialists and graduate students in function theory and in fluid dynamics.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1

Год издания: 1988

Количество страниц: 133

Добавлена в каталог: 20.03.2010

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Предметный указатель

$Cr_{\alpha}(E)$       105
$ex_{\sigma}(n)$       83
$e_{\alpha}$       21
$L(r,\theta)$       105
$L^{1}_{w}(\cdot)$       72
$L^{p}(\cdot)$       68
$L^{\infty}_{real}$       31
$N_{E}(r,\theta)$       105
$T_{n}[a]$       31
$\delta$ -standard kernel      15
$\gamma_{+}(E)$       71
$\hat{\sigma}(I, T, f)$       39
$\hat{\sigma}(T)$       39
$\hat{\sigma}_{C}(\alpha,\beta)$       61
$\hat{\sigma}_{E}(\beta)$       55
$\hat{\tau}(n)$       86
$\iota(\Gamma^{'},\Gamma)$       108
$\omega_{\delta}(K)$       16
$\rho(\Gamma)$       72
$\rho_{+}(\Gamma)$       72
$\Sigma$ -function      35
$\sigma(I,K,f)$       25
$\sigma(k)$       25
$\sigma(n)$       86
$\sigma_{C}(\beta)$       61
$\sigma_{E}(\beta)$       52
$\tilde{C}$       126
$\tilde{\sigma}(I, T, f)$       39
$\tilde{\sigma}(T)$       39
$\tilde{\sigma}(T;\Omega)$       39
$\tilde{\sigma}_{0}(T)$       39
$\tilde{\tau}_{0}(n)$       91
$\xi(E,f)$       118
$\xi(n)$       118
Ahlfors function      80
Analytic capacity $\gamma(E)$       71
Area integral      2
BMO      1
Bu(E)      105

Buffon needle probability      105
Calderon commutator T[a]      1
Calderon — Zygmund decomposition      33
Calderon's problem      82
Calderon's theorem      1
Carleson measure      6
Cauchy transform C      71
Cauchy — Hilbert transform $H_{\Gamma}$       68
Chord-arc curve      68
Coifman — Meyer expression      9
Coifman — Meyer — Stein's theorem      11
Cotlar's lemma      17
Covering lemma      32
Crank      83
Crofton's Formula      105
E[a]      51
Fat crank      99
Galton — Watson process      106
Garabedian function      80
Garnett's example      80
Generalized length      71
Good $\lambda$ inequalities      4
Green's formula      5
Hilbert transform      7
Integralgeometric quantity      105
Interpolation      21
John — Nirenberg's inequality      34
Locally chord-arc      71
Maximal operator M      34
McIntosh expression      13
Poisson kernel      3
Prob      105
Rising Sun Lemma      32
Separation theorem      74
T-atom      11
T-atomic decomposition      13
Tb theorem      15
Tent space      11
Tl theorem      16
Vitushkin's example      80

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