Overview
- Problems of the sort considered in the present monograph profoundly affect the nature of the results in many other adjacent areas of mathematics.
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2142)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces
Book Subtitle: A Sharp Theory
Authors: Ryan Alvarado, Marius Mitrea
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-18132-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-18131-8Published: 25 June 2015
eBook ISBN: 978-3-319-18132-5Published: 09 June 2015
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 486
Number of Illustrations: 5 b/w illustrations, 12 illustrations in colour
Topics: Fourier Analysis, Real Functions, Functional Analysis, Measure and Integration, Partial Differential Equations