Lecture Notes in Mathematics

The Hardy Space H1 with Non-doubling Measures and Their Applications

Authors: YANG, Dachun, Yang, Dongyong, Hu, Guoen

  • The arguments for the main results are detailed and self-contained
  • At least one typical and easily explicable example is given for each important notion further clarifying the relationship between the known and the present notions
  • Detailed references for the content of each chapter are given. Also, well-known related results and some unsolved problems, which will be of interest to the reader, are presented, which might be interesting to the reader
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About this book

The present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems.

The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.

Table of contents (8 chapters)

  • Preliminaries

    Yang, Dachun (et al.)

    Pages 5-22

  • Approximations of the Identity

    Yang, Dachun (et al.)

    Pages 23-58

  • The Hardy Space H 1(μ)

    Yang, Dachun (et al.)

    Pages 59-136

  • The Local Atomic Hardy Space h 1(μ)

    Yang, Dachun (et al.)

    Pages 137-214

  • Boundedness of Operators over $$({\mathbb{R}}^{D},\mu )$$

    Yang, Dachun (et al.)

    Pages 215-328

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-319-00825-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $119.00
price for USA
  • ISBN 978-3-319-00824-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
The Hardy Space H1 with Non-doubling Measures and Their Applications
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2084
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-00825-7
DOI
10.1007/978-3-319-00825-7
Softcover ISBN
978-3-319-00824-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 653
Topics