By Vladimir G. Maz'ya, Tatiana O. Shaposhnikova
The aim of this booklet is to provide a accomplished exposition of the speculation of pointwise multipliers appearing in pairs of areas of differentiable services. the idea was once basically constructed through the authors over the past thirty years and the current quantity is especially in accordance with their effects. half I is dedicated to the idea of multipliers and encloses the subsequent issues: hint inequalities, analytic characterization of multipliers, kinfolk 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 numerous functions of this idea: continuity and compactness of differential operators in pairs of Sobolev areas, multipliers as strategies to linear and quasilinear elliptic equations, larger regularity within the unmarried and double layer capability idea for Lipschitz domain names, regularity of the boundary in $L_p$-theory of elliptic boundary price difficulties, and singular indispensable operators in Sobolev areas.
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