LEADER 05882 am 22009013u 450 001 9910349351603321 005 20200705030210.0 010 $a3-030-02895-X 024 7 $a10.1007/978-3-030-02895-4 035 $a(CKB)4100000008618233 035 $a(DE-He213)978-3-030-02895-4 035 $a(MiAaPQ)EBC5929163 035 $a(Au-PeEL)EBL5929163 035 $a(OCoLC)1132426568 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/37917 035 $a(PPN)237879492 035 $a(EXLCZ)994100000008618233 100 $a20190702d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHardy Inequalities on Homogeneous Groups$b[electronic resource] $e100 Years of Hardy Inequalities /$fby Michael Ruzhansky, Durvudkhan Suragan 205 $a1st ed. 2019. 210 $aCham$cSpringer Nature$d2019 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (XVI, 571 p. 1 illus.) 225 1 $aProgress in Mathematics,$x0743-1643 ;$v327 311 $a3-030-02894-1 327 $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. 330 $aThis open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding. 410 0$aProgress in Mathematics,$x0743-1643 ;$v327 606 $aTopological groups 606 $aLie groups 606 $aPotential theory (Mathematics) 606 $aPartial differential equations 606 $aHarmonic analysis 606 $aFunctional analysis 606 $aDifferential geometry 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aAbstract Harmonic Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12015 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 610 $aMathematics 610 $aTopological groups 610 $aLie groups 610 $aPotential theory (Mathematics) 610 $aPartial differential equations 610 $aHarmonic analysis 610 $aFunctional analysis 610 $aDifferential geometry 615 0$aTopological groups. 615 0$aLie groups. 615 0$aPotential theory (Mathematics). 615 0$aPartial differential equations. 615 0$aHarmonic analysis. 615 0$aFunctional analysis. 615 0$aDifferential geometry. 615 14$aTopological Groups, Lie Groups. 615 24$aPotential Theory. 615 24$aPartial Differential Equations. 615 24$aAbstract Harmonic Analysis. 615 24$aFunctional Analysis. 615 24$aDifferential Geometry. 676 $a512.55 676 $a512.482 700 $aRuzhansky$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut$0950915 702 $aSuragan$b Durvudkhan$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349351603321 996 $aHardy Inequalities on Homogeneous Groups$92149820 997 $aUNINA