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Lecture Notes in Mathematics

Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces

A Sharp Theory

Authors: Alvarado, Ryan, Mitrea, Marius

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  • Problems of the sort considered in the present monograph profoundly affect the nature of the results in many other adjacent areas of mathematics.

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  • ISBN 978-3-319-18132-5
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About this book

Systematically constructing an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Alhlfors-regular quasi-metric spaces. The text is divided into two main parts, with the first part providing atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. The tools established in the first part are then used to develop a sharp theory of Besov and Triebel-Lizorkin spaces in Ahlfors-regular quasi-metric spaces. The monograph is largely self-contained and is intended for mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry.

 

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-319-18132-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.99
price for USA in USD
  • ISBN 978-3-319-18131-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces
Book Subtitle
A Sharp Theory
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2142
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-18132-5
DOI
10.1007/978-3-319-18132-5
Softcover ISBN
978-3-319-18131-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 486
Number of Illustrations
5 b/w illustrations, 12 illustrations in colour
Topics