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Probabilistic Behavior of Harmonic Functions

  • Book
  • © 1999

Overview

Authors:
  1. Rodrigo Bañuelos

    1. Department of Mathematics, Purdue University, West Lafayette, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Charles N. Moore

    1. Department of Mathematics, Kansas State University, Manhattan, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Progress in Mathematics (PM, volume 175)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Basic Ideas and Tools

    • Rodrigo Bañuelos, Charles N. Moore
    Pages 1-44

  3. Decomposition into Martingales: An Invariance Principle

    • Rodrigo Bañuelos, Charles N. Moore
    Pages 45-61

  4. Kolmogorov’s LIL for Harmonic Functions

    • Rodrigo Bañuelos, Charles N. Moore
    Pages 63-92

  5. Sharp Good-λ Inequalities for A and N

    • Rodrigo Bañuelos, Charles N. Moore
    Pages 93-134

  6. Good-λ Inequalities for the Density of the Area Integral

    • Rodrigo Bañuelos, Charles N. Moore
    Pages 135-172

  7. The Classical LIL’s in Analysis

    • Rodrigo Bañuelos, Charles N. Moore
    Pages 173-189

  8. Back Matter

    Pages 191-209
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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

  • Department of Mathematics, Purdue University, West Lafayette, USA

    Rodrigo Bañuelos

  • Department of Mathematics, Kansas State University, Manhattan, USA

    Charles N. Moore

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

  • 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

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