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Table of contents (6 chapters)
Keywords
About this book
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.
Reviews
"The book is devoted to the interplay of potential theory and probability theory…The reader interested in this subject – the interplay of probability theory, harmonic analysis and potential theory – will find a systematic treatment, inspiring both sides, analysis and probability theory."
–Zentralblatt Math
Authors and Affiliations
Bibliographic Information
Book Title: Probabilistic Behavior of Harmonic Functions
Authors: Rodrigo Bañuelos, Charles N. Moore
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-8728-1
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 1999
Hardcover ISBN: 978-3-7643-6062-7Published: 01 August 1999
Softcover ISBN: 978-3-0348-9745-7Published: 06 October 2012
eBook ISBN: 978-3-0348-8728-1Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XIV, 209
Topics: Probability Theory and Stochastic Processes, Analysis