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000727658 1001_ $$aAlvarado, Ryan,$$eauthor.
000727658 24510 $$aHardy spaces on Ahlfors-regular Quasi metric spaces$$h[electronic resource] :$$ba sharp theory /$$cRyan Alvarado, Marius Mitrea.
000727658 264_1 $$aCham :$$bSpringer,$$c[2015]
000727658 264_4 $$c©2015
000727658 300__ $$a1 online resource (viii, 486 pages) :$$billustrations
000727658 336__ $$atext$$2rdacontent
000727658 337__ $$acomputer$$2rdamedia
000727658 338__ $$aonline resource$$2rdacarrier
000727658 347__ $$atext file$$bPDF$$2rda
000727658 4901_ $$aLecture notes in mathematics,$$x1617-9692 ;$$v2142.
000727658 504__ $$aIncludes bibliographical references and indexes.
000727658 5050_ $$aIntroduction. - 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.
000727658 506__ $$aAccess limited to authorized users.
000727658 520__ $$aSystematically 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.
000727658 588__ $$aDescription based on online resource; title from PDF title page (SpringerLink, viewed Jun. 15, 2015)
000727658 650_0 $$aHardy spaces.
000727658 650_0 $$aQuasi-metric spaces.
000727658 7001_ $$aMitrea, Marius,$$eauthor.
000727658 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2142.
000727658 852__ $$bebk
000727658 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-18132-5$$zOnline Access$$91397441.1
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