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＜電子ブック＞
Theory of Sobolev Multipliers : With Applications to Differential and Integral Operators / by Vladimir Maz'ya, Tatyana O. Shaposhnikova
(Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics. ISSN:21969701 ; 337)

版	1st ed. 2009.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XIV, 614 p. 2 illus : online resource
著者標目	*Maz'ya, Vladimir author Shaposhnikova, Tatyana O author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Integral equations LCSH:Differential equations LCSH:Functional analysis FREE:Analysis FREE:Integral Equations FREE:Differential Equations FREE:Functional Analysis
一般注記	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 -- Schrödinger Operator and M(w 1 2 ? w ?1 2) -- Relativistic Schrödinger Operator and M(W ½ 2 ? W ?½ 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 The purpose of this book is to give a comprehensive exposition of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The theory was essentially developed by the authors during the last thirty years and the present volume is mainly based on their results. Part I is devoted to the theory of multipliers and encloses the following topics: trace inequalities, analytic characterization of multipliers, relations between spaces of Sobolev multipliers and other function spaces, maximal subalgebras of multiplier spaces, traces and extensions of multipliers, essential norm and compactness of multipliers, and miscellaneous properties of multipliers. Part II concerns several applications of this theory: continuity and compactness of differential operators in pairs of Sobolev spaces, multipliers as solutions to linear and quasilinear elliptic equations, higher regularity in the single and double layer potential theory for Lipschitz domains, regularity of the boundary in $L_p$-theory of elliptic boundary value problems, and singular integral operators in Sobolev spaces HTTP:URL=https://doi.org/10.1007/978-3-540-69492-2

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