Download E-books Theory of Sobolev Multipliers: With Applications to Differential and Integral Operators (Grundlehren der mathematischen Wissenschaften) PDF

By Vladimir G. Maz'ya, Tatiana O. Shaposhnikova

The aim of this e-book is to provide a entire exposition of the speculation of pointwise multipliers appearing in pairs of areas of differentiable features. the speculation used to be basically built by means of the authors over the past thirty years and the current quantity is especially in keeping with their effects. half I is dedicated to the idea of multipliers and encloses the next issues: hint inequalities, analytic characterization of multipliers, kin among areas of Sobolev multipliers and different functionality areas, maximal subalgebras of multiplier areas, strains and extensions of multipliers, crucial norm and compactness of multipliers, and miscellaneous homes of multipliers. half II matters a number of purposes of this conception: continuity and compactness of differential operators in pairs of Sobolev areas, multipliers as ideas to linear and quasilinear elliptic equations, better regularity within the unmarried and double layer strength conception for Lipschitz domain names, regularity of the boundary in $L_p$-theory of elliptic boundary worth difficulties, and singular critical operators in Sobolev areas.

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