Theory of Sobolev Multipliers

With Applications to Differential and Integral Operators

  • Vladimir G. Maz'ya
  • Tatyana O. Shaposhnikova

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 337)

About this book


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.


Besov spaces Boundary value problem Sobolev space Sobolev spaces boundary and singular integral equations elliptic boundary value problems pointwise multipliers potential spaces

Authors and affiliations

  • Vladimir G. Maz'ya
    • 1
    • 2
  • Tatyana O. Shaposhnikova
    • 2
  1. 1.Department of Mathematical Sciences M&O BuildingUniversity of LiverpoolLiverpoolUK
  2. 2.Department of MathematicsLinküping UniversityLinküpingSweden

Bibliographic information