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The E. M. Stein Lectures on Hardy Spaces

  • Book
  • © 2023

Overview

Authors:
  1. Steven G. Krantz

    1. Department of Mathematics, Washington University, St. Louis, USA

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  • Captures a course given by Elias M. Stein in 1973-1974
  • Represents the point of view of a major figure in twentieth-century harmonic analysis
  • Offers a unique insight into real variable Hardy spaces from one of the originators

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2326)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Introductory Material

    • Steven Krantz
    Pages 1-34

  3. More on Hardy Spaces

    • Steven Krantz
    Pages 35-71

  4. Background on Hp Spaces

    • Steven Krantz
    Pages 73-100

  5. Hardy Spaces on D

    • Steven Krantz
    Pages 101-135

  6. Hardy Spaces on \( \mathbb {R}^n\)

    • Steven Krantz
    Pages 137-225

  7. Developments Since 1974

    • Steven Krantz
    Pages 227-241

  8. Concluding Remarks

    • Steven Krantz
    Pages 243-243

  9. Back Matter

    Pages 245-253
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Keywords

About this book

​The book The E. M. Stein Lectures on Hardy Spaces is based on a graduate course on real variable Hardy spaces which was given by E.M. Stein at Princeton University in the academic year 1973-1974. Stein, along with C. Fefferman and G. Weiss, pioneered this subject area, removing the theory of Hardy spaces from its traditional dependence on complex variables, and to reveal its real-variable underpinnings.

This book is based on Steven G. Krantz’s notes from the course given by Stein. The text builds on Fefferman's theorem that BMO is the dual of the Hardy space. Using maximal functions, singular integrals, and related ideas, Stein offers many new characterizations of the Hardy spaces. The result is a rich tapestry of ideas that develops the theory of singular integrals to a new level. The final chapter describes the major developments since 1974.

This monograph is of broad interest to graduate students and researchers in mathematical analysis. Prerequisites for the book include a solid understanding of real variable theory and complex variable theory. A basic knowledge of functional analysis would also be useful.

Authors and Affiliations

  • Department of Mathematics, Washington University, St. Louis, USA

    Steven G. Krantz

About the author

Steven G. Krantz was born in San Francisco, California in 1951. He received the B.A. degree from the University of California at Santa Cruz in 1971 and the Ph.D. from Princeton University in 1974. Krantz has taught at UCLA, Princeton University, Penn State, and Washington University in St. Louis. He was Chair of the latter department for five years. Krantz has had 9 Masters students and 20 Ph.D. students. He has written more than 135 books and more than 270 scholarly papers. He edits 5 journals, and is Managing Editor of 3. He is the founding editorof the Journal of Geometric Analysis. He is the creator, founder, and editor of the new journal Complex Analysis and its Synergies. Krantz has won the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize. He was recently named to the Sequoia High School Hall of Fame. He is an AMS Fellow.


Bibliographic Information

  • Book Title: The E. M. Stein Lectures on Hardy Spaces

  • Authors: Steven G. Krantz

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-21952-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Softcover ISBN: 978-3-031-21951-1Published: 10 February 2023

  • eBook ISBN: 978-3-031-21952-8Published: 09 February 2023

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 253

  • Number of Illustrations: 43 b/w illustrations

  • Topics: Fourier Analysis, Potential Theory

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