Probabilistic Behavior of Harmonic Functions
By: by Rodrigo Bañuelos, Charles N. Moore
Contributors: Moore, Charles N.
Series: Progress in Mathematics -- 175; Progress in Mathematics -- 175
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 1999
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 209
ISBN-13: 9783034897457; 9783034887281
Subjects: Mathematics
Description: Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful. This monograph, aimed at researchers and students in these fields, explores several aspects of this relationship. The primary focus of the text is the nontangential maximal function and the area function of a harmonic function and their probabilistic analogues in martingale theory. The text first gives the requisite background material from harmonic analysis and discusses known results concerning the nontangential maximal function and area function, as well as the central and essential role these have played in the development of the field.The book next discusses further refinements of traditional results: among these are sharp good-lambda inequalities and laws of the iterated logarithm involving nontangential maximal functions and area functions. Many applications of these results are given. Throughout, the constant interplay between probability and harmonic analysis is emphasized and explained. The text contains some new and many recent results combined in a coherent presentation.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.