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001 978-3-319-18132-5
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005 20190213151920.0
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008 150609s2015 gw | s |||| 0|eng d
020 _a9783319181325
_9978-3-319-18132-5
024 7 _a10.1007/978-3-319-18132-5
_2doi
050 4 _aQA403.5-404.5
072 7 _aPBKF
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.2433
_223
100 1 _aAlvarado, Ryan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aHardy Spaces on Ahlfors-Regular Quasi Metric Spaces
_h[electronic resource] :
_bA Sharp Theory /
_cby Ryan Alvarado, Marius Mitrea.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aVIII, 486 p. 17 illus., 12 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2142
505 0 _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.
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.
650 0 _aFourier analysis.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aDifferential equations, partial.
650 1 4 _aFourier Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12058
650 2 4 _aReal Functions.
_0http://scigraph.springernature.com/things/product-market-codes/M12171
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aMeasure and Integration.
_0http://scigraph.springernature.com/things/product-market-codes/M12120
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
700 1 _aMitrea, Marius.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319181332
776 0 8 _iPrinted edition:
_z9783319181318
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2142
856 4 0 _uhttps://doi.org/10.1007/978-3-319-18132-5
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c12316
_d12316