Square Functions and the \(A_\infty \) Property of Elliptic Measures

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• 作者：C. Kenig ; B. Kirchheim ; J. Pipher ; T. Toro
• 刊名：Journal of Geometric Analysis
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：26
• 期：3
• 页码：2383-2410
• 全文大小：604 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X
• 卷排序：26

文摘

In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, nonsymmetric divergence form operators. We will show that a certain optimal Carleson measure estimate for bounded solutions of such operators implies a regularity result for the associated elliptic measure.KeywordsElliptic measureSolvability of the Dirichlet problemSquare functions\(A_\infty \) - weights