Theory of Sobolev Multipliers

From the reviews: This very interesting book collects the multitude of new results in this area, essentially obtained by the authors or inspired by their work during the past thirty years. This comprehensive monograph is very well written and structured. It will certainly become an extremely useful reference for mathematicians working in functional analysis and in the theories of partial differential, integral, and pseudodifferential operators. it recommendable both for experts and mathematicians with a wider field of interest. (Dorothee D. Haroske, Mathematical Reviews, Issue 2010 d) The main goal of Sobolev Multipliers is to present complete characterizations and applications of multipliers Mf acting from a Sobolev space . it will be of interest to a great variety of serious readers, from graduate students to experts in analysis as well as mathematical physicists, differential geometers, and applied mathematicians. a valuable reference and guide to the literature, as well as a unique collection of methods and resultsindispensable for anyone who is using Sobolev spaces in their work. (I. E. Verbitsky, Bulletin of the American Mathematical Society, Vol. 48 (1), January, 2011)

Vladimir Maz'ya is a professor at the University of Liverpool and professor emeritus at Linkoeping University, a member of the Royal Swedish Academy of Sciences. In 2004 he was awarded the Celsius medal in gold for his outstanding contributions to the theory of partial differential equations and hydrodynamics. Maz'ya published over 400 papers and 15 books in various domains of the theory of differential equations, functional analysis, approximation theory, numerical methods, and applications to mechanics and mathematical physics (for more information see www.mai.liu.se/~vlmaz). Tatyana Shaposhnikova is a professor at Linkoeping University. She works in function theory, functional analysis and their applications to partial differential and integral equations. The list of her publications contain three books and more than 70 articles. Together with V. Maz'ya she was awarded the Verdaguer Prize of the French Academy of Sciences in 2003 (for more information see www.mai.liu.se/~tasha).

Description 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.- Schrdinger Operator and M(w 1 2 ? w ?1 2).- Relativistic Schrdinger Operator and M(W 2 ? W ? 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.