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Inequalities: A Journey into Linear Analysis by D. J. H. Garling (Hardcover, 2007)

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9780521876247, Cambridge University Press. D. J. H. Garling (Author). This book 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.