Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces: A Sharp Theory

Author:   Ryan Alvarado ,  Marius Mitrea
Publisher:   Springer International Publishing AG
Edition:   2015 ed.
Volume:   2142
ISBN:  

9783319181318


Pages:   486
Publication Date:   25 June 2015
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces: A Sharp Theory


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Overview

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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Author:   Ryan Alvarado ,  Marius Mitrea
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   2015 ed.
Volume:   2142
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   7.431kg
ISBN:  

9783319181318


ISBN 10:   3319181319
Pages:   486
Publication Date:   25 June 2015
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

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