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000899210 019__ $$a1107874648$$a1109817024$$a1110327836
000899210 020__ $$a9783030028954$$q(electronic book)
000899210 020__ $$a303002895X$$q(electronic book)
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000899210 0248_ $$a10.1007/978-3-030-02
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000899210 1001_ $$aRuzhansky, Michael,$$eauthor.
000899210 24510 $$aHardy inequalities on homogeneous groups :$$b100 years of Hardy inequalities /$$cMichael Ruzhansky, Durvudkhan Suragan.
000899210 264_1 $$aCham, Switzerland :$$bBirkhäuser,$$c[2019]
000899210 300__ $$a1 online resource
000899210 336__ $$atext$$btxt$$2rdacontent
000899210 337__ $$acomputer$$bc$$2rdamedia
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000899210 4901_ $$aProgress in mathematics ;$$vvolume 327
000899210 504__ $$aIncludes bibliographical references and index.
000899210 5050_ $$aIntroduction -- Analysis on Homogeneous Groups -- Hardy Inequalities on Homogeneous Groups -- Rellich, Caarelli-Kohn-Nirenberg, and Sobolev Type Inequalities -- Fractional Hardy Inequalities -- Integral Hardy Inequalities on Homogeneous Groups -- Horizontal Inequalities on Stratied Groups -- Hardy-Rellich Inequalities and Fundamental Solutions -- Geometric Hardy Inequalities on Stratied Groups -- Uncertainty Relations on Homogeneous Groups -- Function Spaces on Homogeneous Groups -- Elements of Potential Theory on Stratified Groups -- Hardy and Rellich Inequalities for Sums of Squares -- Bibliography -- Index.
000899210 506__ $$aAccess limited to authorized users.
000899210 520__ $$aThis open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
000899210 588__ $$aDescription based on online resource; title from digital title page (viewed on August 09, 2019).
000899210 650_0 $$aTopological groups.
000899210 650_0 $$aPotential theory (Mathematics)
000899210 650_0 $$aDifferential equations, Partial.
000899210 650_0 $$aHarmonic analysis.
000899210 650_0 $$aFunctional analysis.
000899210 650_0 $$aGlobal differential geometry.
000899210 7001_ $$aSuragan, Durvudkhan,$$eauthor.
000899210 77608 $$iPrint version: $$z3030028941$$z9783030028947$$w(OCoLC)1054366195
000899210 830_0 $$aProgress in mathematics (Boston, Mass.) ;$$v327.
000899210 852__ $$bebk
000899210 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-02895-4$$zOnline Access$$91397441.1
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