MOMENTAN AUSVERKAUFT
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Product Identifiers
PublisherSpringer International Publishing A&G
ISBN-103319181319
ISBN-139783319181318
eBay Product ID (ePID)211216397
Product Key Features
Number of PagesVIII, 486 Pages
Publication NameHardy Spaces on Ahlfors-Regular Quasi Metric Spaces : a Sharp Theory
LanguageEnglish
SubjectDifferential Equations / General, Functional Analysis, Topology, Mathematical Analysis, Complex Analysis
Publication Year2015
TypeTextbook
AuthorRyan Alvarado, Marius Mitrea
Subject AreaMathematics
SeriesLecture Notes in Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Weight262.1 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2015-940436
Dewey Edition23
Series Volume Number2142
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515.94
Table Of ContentIntroduction. - Geometry of Quasi-Metric Spaces.- Analysis on Spaces of Homogeneous Type.- Maximal Theory of Hardy Spaces.- Atomic Theory of Hardy Spaces.- Molecular and Ionic Theory of Hardy Spaces.- Further Results.- Boundedness of Linear Operators Defined on Hp(X).- Besov and Triebel-Lizorkin Spaces on Ahlfors-Regular Quasi-Metric Spaces.
SynopsisSystematically 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.
LC Classification NumberQA403.5-404.5
