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020 _a9783030028954
_9978-3-030-02895-4
024 7 _a10.1007/978-3-030-02895-4
_2doi
050 4 _aQA252.3
050 4 _aQA387
072 7 _aPBG
_2bicssc
072 7 _aMAT014000
_2bisacsh
072 7 _aPBG
_2thema
082 0 4 _a512.55
_223
082 0 4 _a512.482
_223
100 1 _aRuzhansky, Michael.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aHardy Inequalities on Homogeneous Groups
_h[electronic resource] :
_b100 Years of Hardy Inequalities /
_cby Michael Ruzhansky, Durvudkhan Suragan.
250 _a1st ed. 2019.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2019.
300 _aXVI, 571 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics,
_x0743-1643 ;
_v327
505 0 _aIntroduction -- Analysis on Homogeneous Groups -- Hardy Inequalities on Homogeneous Groups -- Rellich, Caarelli-Kohn-Nirenberg, and Sobolev Type Inequalities -- Fractional Hardy Inequalities -- Integral Hardy Inequalities on Homogeneous Groups -- Horizontal Inequalities on Stratied Groups -- Hardy-Rellich Inequalities and Fundamental Solutions -- Geometric Hardy Inequalities on Stratied Groups -- Uncertainty Relations on Homogeneous Groups -- Function Spaces on Homogeneous Groups -- Elements of Potential Theory on Stratified Groups -- Hardy and Rellich Inequalities for Sums of Squares -- Bibliography -- Index.
506 0 _aOpen Access
520 _aThis open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
650 0 _aTopological groups.
650 0 _aLie groups.
650 0 _aPotential theory (Mathematics).
650 0 _aPartial differential equations.
650 0 _aHarmonic analysis.
650 0 _aFunctional analysis.
650 0 _aDifferential geometry.
650 1 4 _aTopological Groups, Lie Groups.
_0http://scigraph.springernature.com/things/product-market-codes/M11132
650 2 4 _aPotential Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12163
650 2 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aAbstract Harmonic Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12015
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
700 1 _aSuragan, Durvudkhan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783030028947
776 0 8 _iPrinted edition:
_z9783030028961
830 0 _aProgress in Mathematics,
_x0743-1643 ;
_v327
856 4 0 _uhttps://doi.org/10.1007/978-3-030-02895-4
912 _aZDB-2-SMA
912 _aZDB-2-SOB
999 _c524152
_d524150