'I never heard of "Ugli?cation," Alice ventured to say. 'What is it?" Lewis Carroll, "Alice in Wonderland" Subject and motivation. The present book is devoted to a theory of m- tipliers in spaces of di?erentiable functions and its applications to analysis, partial di?erential and integral equations. By a multiplier acting from one functionspaceS intoanotherS ,wemeanafunctionwhichde?nesabounded 1 2 linear mapping ofS intoS by pointwise multiplication. Thus with any pair 1 2 of spacesS ,S we associate a third one, the space of multipliersM(S?S ) 1 2 1 2 endowed with the norm of the operator of multiplication. In what follows, the role of the spacesS andS is played by Sobolev spaces, Bessel potential 1 2 spaces, Besov spaces, and the like. The Fourier multipliers are not dealt with in this book. In order to emp- size the di?erence between them and the multipliers under consideration, we attach Sobolev's name to the latter. By coining the term Sobolev multipliers we just hint at various spaces of di?erentiable functions of Sobolev's type, being fully aware that Sobolev never worked on multipliers. After all, Fourier never did either.
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN: 9783642089022
Number of pages: 614
Dimensions: 235 x 155 mm
Language: English
Edition: Softcover reprint of hardcover 1st ed. 2009
From the reviews: "This very interesting book ... collects the multitude of new results in this area, essentially obtained by the authors or inspired by their work during the past thirty years. ... This comprehensive monograph is very well written and structured. It will certainly become an extremely useful reference for mathematicians working in functional analysis and in the theories of partial differential, integral, and pseudodifferential operators. ... it recommendable both for experts and mathematicians with a wider field of interest." (Dorothee D. Haroske, Mathematical Reviews, Issue 2010 d) "The main goal of Sobolev Multipliers is to present complete characterizations and applications of multipliers Mf acting from a Sobolev space ... . it will be of interest to a great variety of serious readers, from graduate students to experts in analysis ... as well as mathematical physicists, differential geometers, and applied mathematicians. ... a valuable reference and guide to the literature, as well as a unique collection of methods and results-indispensable for anyone who is using Sobolev spaces in their work." (I. E. Verbitsky, Bulletin of the American Mathematical Society, Vol. 48 (1), January, 2011)
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