國立虎尾科技大學 |

Hardy Inequalities on Homogeneous Groups = 100 Years of Hardy Inequalities /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Hardy Inequalities on Homogeneous Groups/ by Michael Ruzhansky, Durvudkhan Suragan.
Reminder of title:	100 Years of Hardy Inequalities /
Author:	Ruzhansky, Michael.
other author:	Suragan, Durvudkhan.
Description:	XVI, 571 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Topological groups. -
Online resource:	https://doi.org/10.1007/978-3-030-02895-4
ISBN:	9783030028954

Hardy Inequalities on Homogeneous Groups = 100 Years of Hardy Inequalities /
Ruzhansky, Michael.

Hardy Inequalities on Homogeneous Groups100 Years of Hardy Inequalities /[electronic resource] :by Michael Ruzhansky, Durvudkhan Suragan. - 1st ed. 2019. - XVI, 571 p. 1 illus.online resource. - Progress in Mathematics,3270743-1643 ;. - Progress in Mathematics,312.

Introduction -- 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.

Open Access

This 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.

ISBN: 9783030028954

Standard No.: 10.1007/978-3-030-02895-4doiSubjects--Topical Terms:

885827
Topological groups.

LC Class. No.: QA252.3

Dewey Class. No.: 512.55

Hardy Inequalities on Homogeneous Groups = 100 Years of Hardy Inequalities /
LDR:03919nam a22004455i 4500 001 1005894
003 DE-He213
005 20200705030210.0
007 cr nn 008mamaa
008 210106s2019 gw | s |||| 0|eng d
020 $a 9783030028954 $9 978-3-030-02895-4
024 7 $a 10.1007/978-3-030-02895-4 $2 doi
035 $a 978-3-030-02895-4
050 4 $a QA252.3
050 4 $a QA387
072 7 $a PBG $2 bicssc
072 7 $a MAT014000 $2 bisacsh
072 7 $a PBG $2 thema
082 0 4 $a 512.55 $2 23
082 0 4 $a 512.482 $2 23
100 1 $a Ruzhansky, Michael. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 788073
245 1 0 $a Hardy Inequalities on Homogeneous Groups $h [electronic resource] : $b 100 Years of Hardy Inequalities / $c by Michael Ruzhansky, Durvudkhan Suragan.
250 $a 1st ed. 2019.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2019.
300 $a XVI, 571 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Progress in Mathematics, $x 0743-1643 ; $v 327
505 0 $a Introduction -- 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 $a Open Access
520 $a This 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 $a Topological groups. $3 885827
650 0 $a Lie groups. $3 527929
650 0 $a Potential theory (Mathematics). $3 1255004
650 0 $a Partial differential equations. $3 1102982
650 0 $a Harmonic analysis. $3 672073
650 0 $a Functional analysis. $3 527706
650 0 $a Differential geometry. $3 882213
650 1 4 $a Topological Groups, Lie Groups. $3 672074
650 2 4 $a Potential Theory. $3 672266
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Abstract Harmonic Analysis. $3 672075
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Differential Geometry. $3 671118
700 1 $a Suragan, Durvudkhan. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1299352
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030028947
776 0 8 $i Printed edition: $z 9783030028961
830 0 $a Progress in Mathematics, $x 0743-1643 ; $v 312 $3 1258196
856 4 0 $u https://doi.org/10.1007/978-3-030-02895-4
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
912 $a ZDB-2-SOB
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)