Probabilistic Behavior of Harmonic Functions

Rodrigo Banuelos

ISBN 10: 3764360623 / ISBN 13: 9783764360627

Published by Birkhäuser, Birkhäuser, 1999

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783764360627

Bibliographic Details

• Title: Probabilistic Behavior of Harmonic Functions
• Publisher: Birkhäuser, Birkhäuser
• Publication Date: 1999
• Language: English
• ISBN 10: 3764360623
• ISBN 13: 9783764360627
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 17D millimeters 241 millimeters width by 160 millimeters height by 17 millimeters depth
• Weight: 512 grams

About this title

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.

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