Probabilistic Behavior of Harmonic Functions: 175 (Progress in Mathematics, 175) - Hardcover

Banuelos, Rodrigo; Moore, Charles N.

Hardcover

ISBN 10: 3764360623 ISBN 13: 9783764360627

Publisher: Birkhäuser, 1999

Synopsis

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.

About this title

Review

"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

Synopsis

Harmonic analysis and probability have enjoyed a mutually beneficial relationship. This monograph explores several aspects of this relationship. The primary focus of the text is the nonangential maximal function and the area function of a harmonic function and their probablistic analogues in martingale theory.

Edition details

• Publisher: Birkhäuser
• Publication date: 1999
• Language: English
• ISBN 10: 3764360623
• ISBN 13: 9783764360627
• Binding: Hardcover
• Number of pages: 223