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Inequalities A Journey into Linear Analysis

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ISBN-10: 0521876249

ISBN-13: 9780521876247

Edition: 2007

Authors: Garling D. J. H.

List price: $174.99
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Description:

Contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue…    
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Book details

List price: $174.99
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 7/5/2007
Binding: Hardcover
Pages: 346
Size: 7.00" wide x 9.75" long x 1.00" tall
Weight: 1.628

D. J. H. Garling is an Emeritus Reader in Mathematical Analysis at the University of Cambridge and a Fellow of St John's College, Cambridge.

Introduction
Measure and integral
The Cauchy-Schwarz inequality
The AM-GM inequality
Convexity, and Jensen's inequality
The Lp spaces
Banach function spaces
Rearrangements
Maximal inequalities
Complex interpolation
Real interpolation
The Hilbert transform, and Hilbert's inequalities
Khintchine's inequality
Hypercontractive and logarithmic Sobolev inequalities
Hadamard's inequality
Hilbert space operator inequalities
Summing operators
Approximation numbers and eigenvalues
Grothendieck's inequality, type and cotype.