© 1999

Probabilistic Behavior of Harmonic Functions


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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Rodrigo Bañuelos, Charles N. Moore
    Pages 1-44
  3. Rodrigo Bañuelos, Charles N. Moore
    Pages 45-61
  4. Rodrigo Bañuelos, Charles N. Moore
    Pages 63-92
  5. Rodrigo Bañuelos, Charles N. Moore
    Pages 93-134
  6. Rodrigo Bañuelos, Charles N. Moore
    Pages 135-172
  7. Rodrigo Bañuelos, Charles N. Moore
    Pages 173-189
  8. Back Matter
    Pages 191-209

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.


Maxima Maximum Poisson kernel Probability Singular integral Variance calculus harmonic analysis logarithm

Authors and affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsKansas State UniversityManhattanUSA

Bibliographic information

  • Book Title Probabilistic Behavior of Harmonic Functions
  • Authors Rodrigo Banuelos
    Charles N. Moore
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Birkhäuser Verlag 1999
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-6062-7
  • Softcover ISBN 978-3-0348-9745-7
  • eBook ISBN 978-3-0348-8728-1
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XIV, 209
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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"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