Theory of Sobolev Multipliers: With Applications to Differential and Integral Operators (Grundlehren der mathematischen Wissenschaften, 337) - Hardcover

Maz'ya, Vladimir; Shaposhnikova, Tatyana O.

Hardcover

ISBN 10: 3540694900 ISBN 13: 9783540694908

Publisher: Springer, 2008

Synopsis

The first part of this book offers a comprehensive overview of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The second part of the book explores several applications of this theory.

About this title

From the Back Cover:

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.

About the Author:

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).

About this edition

• Publisher: Springer
• Publication date: 2008
• ISBN 10: 3540694900
• ISBN 13: 9783540694908
• Binding: Hardcover
• Number of pages: 628