Theory of Sobolev multipliers : with applications to differential and integral operators
著者
書誌事項
Theory of Sobolev multipliers : with applications to differential and integral operators
（Die Grundlehren der mathematischen Wissenschaften, v. 337）
Springer, c2009
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注記
Includes bibliographical references (p. 591-603) and index
内容説明・目次
内容説明
'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.
目次
Description and Properties of Multipliers.- Trace Inequalities for Functions in Sobolev Spaces.- Multipliers in Pairs of Sobolev Spaces.- Multipliers in Pairs of Potential Spaces.- The Space M(B m p ? B l p ) with p > 1.- The Space M(B m 1 ? B l 1).- Maximal Algebras in Spaces of Multipliers.- Essential Norm and Compactness of Multipliers.- Traces and Extensions of Multipliers.- Sobolev Multipliers in a Domain, Multiplier Mappings and Manifolds.- Applications of Multipliers to Differential and Integral Operators.- Differential Operators in Pairs of Sobolev Spaces.- Schroedinger Operator and M(w 1 2 ? w ?1 2).- Relativistic Schroedinger Operator and M(W 1/2 2 ? W ?1/2 2).- Multipliers as Solutions to Elliptic Equations.- Regularity of the Boundary in L p -Theory of Elliptic Boundary Value Problems.- Multipliers in the Classical Layer Potential Theory for Lipschitz Domains.- Applications of Multipliers to the Theory of Integral Operators.
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