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010   $a3-319-18132-7
024 7 $a10.1007/978-3-319-18132-5
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100   $a20150609d2015      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aHardy Spaces on Ahlfors-Regular Quasi Metric Spaces $eA Sharp Theory /$fby Ryan Alvarado, Marius Mitrea
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (VIII, 486 p. 17 illus., 12 illus. in color.) 
225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2142
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-18131-9 
327   $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.
330   $aSystematically building an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Ahlfors-regular quasi-metric spaces. The text is broadly divided into two main parts. The first part gives atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. The tools established in the first part are then used to develop a sharp theory of Besov and Triebel-Lizorkin spaces in Ahlfors-regular quasi-metric spaces. The monograph is largely self-contained and is intended for an audience of mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry.
410  0$aLecture Notes in Mathematics,$x1617-9692 ;$v2142
606   $aFourier analysis
606   $aFunctions of real variables
606   $aFunctional analysis
606   $aMeasure theory
606   $aDifferential equations
606   $aFourier Analysis
606   $aReal Functions
606   $aFunctional Analysis
606   $aMeasure and Integration
606   $aDifferential Equations
615  0$aFourier analysis.
615  0$aFunctions of real variables.
615  0$aFunctional analysis.
615  0$aMeasure theory.
615  0$aDifferential equations.
615 14$aFourier Analysis.
615 24$aReal Functions.
615 24$aFunctional Analysis.
615 24$aMeasure and Integration.
615 24$aDifferential Equations.
676   $a515.94
700   $aAlvarado$b Ryan$4aut$4http://id.loc.gov/vocabulary/relators/aut$0716353
702   $aMitrea$b Marius$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910131386903321
996   $aHardy Spaces on Ahlfors-Regular Quasi Metric Spaces$92247672
997   $aUNINA