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＜電子ブック＞
Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces : A Sharp Theory / by Ryan Alvarado, Marius Mitrea
(Lecture Notes in Mathematics. ISSN:16179692 ; 2142)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
本文言語	英語
大きさ	VIII, 486 p. 17 illus., 12 illus. in color : online resource
著者標目	*Alvarado, Ryan author Mitrea, Marius author SpringerLink (Online service)
件　名	LCSH:Fourier analysis LCSH:Functions of real variables LCSH:Functional analysis LCSH:Measure theory LCSH:Differential equations FREE:Fourier Analysis FREE:Real Functions FREE:Functional Analysis FREE:Measure and Integration FREE:Differential Equations
一般注記	Introduction. - 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 Systematically building an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Ahlfors-regular quasi-metric spaces. The text is broadly divided into two main parts. The first part gives 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 an audience of mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry HTTP:URL=https://doi.org/10.1007/978-3-319-18132-5

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