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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An inequality for the distribution of the Brownian gradient function


Author: Burgess Davis
Journal: Proc. Amer. Math. Soc. 37 (1973), 189-194
MSC: Primary 60J65; Secondary 30A78, 31A05
DOI: https://doi.org/10.1090/S0002-9939-1973-0373036-0
MathSciNet review: 0373036
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Abstract: The Brownian gradient function of a harmonic function u in the unit disc is shown to be distributionally about as large as the classical area function of u. This distribution function inequality strengthens some integral inequalities of Burkholder and Gundy.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0373036-0
Keywords: Harmonic function, area function, Brownian motion, distribution inequality
Article copyright: © Copyright 1973 American Mathematical Society