Theory of Sobolev Multipliers : With Applications to Differential and Integral Operators

Vladimir Maz'ya

ISBN 10: 3540694900 / ISBN 13: 9783540694908

Edité par Springer, Springer Spektrum, 2008

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - 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.

N° de réf. du vendeur 9783540694908

Détails bibliographiques

• Titre: Theory of Sobolev Multipliers : With Applications to Differential and Integral Operators
• Éditeur: Springer, Springer Spektrum
• Date de parution: 2008
• Langue: anglais
• ISBN à 10 chiffres: 3540694900
• ISBN à 13 chiffres: 9783540694908
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 38 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 38 millimètres de profondeur
• Poids: 1098 grammes

A propos de ce titre

Synopsis

'I never heard of "Ugli?cation," Alice ventured to say. 'What is it?'' Lewis Carroll, "Alice in Wonderland" Subject and motivation. The present book is devoted to a theory of m- tipliers in spaces of di?erentiable functions and its applications to analysis, partial di?erential and integral equations. By a multiplier acting from one functionspaceS intoanotherS, wemeanafunctionwhichde?nesabounded 1 2 linear mapping ofS intoS by pointwise multiplication. Thus with any pair 1 2 of spacesS, S we associate a third one, the space of multipliersM(S?S ) 1 2 1 2 endowed with the norm of the operator of multiplication. In what follows, the role of the spacesS andS is played by Sobolev spaces, Bessel potential 1 2 spaces, Besov spaces, and the like. The Fourier multipliers are not dealt with in this book. In order to emp- size the di?erence between them and the multipliers under consideration, we attach Sobolev's name to the latter. By coining the term Sobolev multipliers we just hint at various spaces of di?erentiable functions of Sobolev's type, being fully aware that Sobolev never worked on multipliers. After all, Fourier never did either.

À propos de l?auteur

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).