03411nmm a2200361 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245016300160250001700323260006300340300004100403505096900444653002401413653003601437653002301473653002401496653003501520653002301555653003401578653001301612700004001625710003401665041001901699989003601718490010001754856007201854082000801926520111501934EB000378010EBX0100000000000000023106200000000000000.0cr|||||||||||||||||||||130626 ||| eng a97835406949221 aMaz'ya, Vladimir00aTheory of Sobolev MultipliershElektronische RessourcebWith Applications to Differential and Integral Operatorscby Vladimir Maz'ya, Tatyana O. Shaposhnikova a1st ed. 2009 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2009, 2009 aXIV, 614 p. 2 illusbonline resource0 aDescription 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 aFunctional analysis aDifferential equations, partial aIntegral equations aFunctional Analysis aPartial Differential Equations aIntegral Equations aGlobal analysis (Mathematics) aAnalysis1 aShaposhnikova, Tatyana O.e[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics uhttps://doi.org/10.1007/978-3-540-69492-2?nosfx=yxVerlag3Volltext0 a515 aThe 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