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Distribution function inequalities for the area integral

  • Burgess Davis
  • Renming Song
Chapter
Part of the Selected Works in Probability and Statistics book series (SWPS)

Abstract

Let A be the area integral of a function u harmonic in the Euclidean half-space R n x (0, ∞). Information about the distribution function of a localized version of A is obtained that leads to a general integral inequality between A and the nontangential maximal function of u and provides a convenient approach to the study of the pointwise behavior of u near the boundary. In addition, the general integral inequality of [2] between the nontangential maximal function of u and that of a properly chosen conjugate is shown to hold also in the case n > 1.

Keywords

Harmonic Function Boundary Point Maximal Function Lipschitz Domain Measurable Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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