By Vladimir G. Maz'ya, Tatiana O. Shaposhnikova
The aim of this publication is to provide a entire exposition of the speculation of pointwise multipliers appearing in pairs of areas of differentiable services. the idea used to be primarily constructed by means of the authors over the last thirty years and the current quantity is especially in response to their effects. half I is dedicated to the idea of multipliers and encloses the next subject matters: hint inequalities, analytic characterization of multipliers, kinfolk among areas of Sobolev multipliers and different functionality areas, maximal subalgebras of multiplier areas, lines and extensions of multipliers, crucial norm and compactness of multipliers, and miscellaneous homes of multipliers. half II issues numerous functions of this concept: continuity and compactness of differential operators in pairs of Sobolev areas, multipliers as recommendations to linear and quasilinear elliptic equations, greater regularity within the unmarried and double layer capability concept for Lipschitz domain names, regularity of the boundary in $L_p$-theory of elliptic boundary price difficulties, and singular critical operators in Sobolev areas.
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