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Author Ruzhansky, M. (Michael), author.

Title Hardy inequalities on homogeneous groups : 100 years of Hardy inequalities / Michael Ruzhansky, Durvudkhan Suragan.

Publication Info. Cham, Switzerland : Birkhäuser, [2019]

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 University of Saint Joseph: Pope Pius XII Library - Internet  WORLD WIDE WEB E-BOOK Springer    Downloadable
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Description 1 online resource.
Series Progress in mathematics ; volume 327
Progress in mathematics (Boston, Mass.) ; 327. 0743-1643
Bibliography Includes bibliographical references and index.
Access Open Access.
Contents 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.
Summary 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.
Note Description based on online resource; title from digital title page (viewed on August 09, 2019).
Local Note SpringerLink Springer Nature Open Access eBooks
Subject Topological groups.
Potential theory (Mathematics)
Differential equations, Partial.
Harmonic analysis.
Functional analysis.
Global differential geometry.
Topological Groups, Lie Groups. http://scigraph.springernature.com/things/product-market-codes/M11132
Potential Theory. http://scigraph.springernature.com/things/product-market-codes/M12163
Differential equations, Partial. http://id.loc.gov/authorities/subjects/sh85037912
Abstract Harmonic Analysis. http://scigraph.springernature.com/things/product-market-codes/M12015
Functional analysis. http://id.loc.gov/authorities/subjects/sh85052312
Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146
Differential equations, Partial. (OCoLC)fst00893484
Functional analysis. (OCoLC)fst00936061
Global differential geometry. (OCoLC)fst00943477
Harmonic analysis. (OCoLC)fst00951490
Potential theory (Mathematics) (OCoLC)fst01073489
Topological groups. (OCoLC)fst01152684
Added Author Suragan, Durvudkhan, author.
Other Form: Original 3030028941 9783030028947 (OCoLC)1054366195
ISBN 9783030028954 electronic book
303002895X electronic book
9783030028947
3030028941
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