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Differential Subordination of Harmonic Functions and Martingales

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

Abstract

A fruitful analogy in harmonic analysis is the analogy between a conjugate harmonic function and a martingale transform. One idea that underlies both of these concepts is the idea of differential subordination. Our study of it here yields new information about harmonic functions and martingales, and their interaction.

Keywords

Banach Space Harmonic Function Hardy Space Harmonic Measure Complex Hilbert Space 
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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