Maz'ya / Shaposhnikova Theory of Sobolev Multipliers

With Applications to Differential and Integral Operators
1. Auflage 2008
ISBN: 978-3-540-69492-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 337, 614 Seiten, eBook

Reihe: Grundlehren der mathematischen Wissenschaften

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.

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).

Zielgruppe

Research

Autoren/Hrsg.

Maz'ya, Vladimir

Shaposhnikova, Tatyana O.

Inhaltsverzeichnis

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.- Schrödinger Operator and M(w 1 2 ? w ?1 2).- Relativistic Schrödinger Operator and M(W ½ 2 ? W ?½ 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.

Über Autor(innen)

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).