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内容説明
Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function， also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.
This second edition of Adam’s ’classic’ reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.
* Self-contained and accessible for readers in other disciplines.
* Written at elementary level making it accessible to graduate students.
From the Back Cover
This book can be highly recommended to every reader interested in functional analysis and its applications (MathSciNet on Sobolev Spaces， First Edition) Sobolev Spaces presents an introduction to the theory of Sobolev spaces and related spaces of function of several real variables， especially the imbedding characteristics of these spaces. This theory is widely used in Pure and Applied Mathematics and the Physical Sciences. This second edition of Adams’ classic reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike. Key Features · Self-contained and accessible for readers in other disciplines. · Written at elementary level making it accessible to graduate students. · Includes reviews of real analysis and an extensive treatment of Lebesgue spaces. · Develops at length the intrinsic definition and properties of Sobolev spaces， in particular their imbedding， compact imbedding， interpolation and extension properties. · Provides a thorough treatment of the real interpolation method and its application to Lorentz and Besov spaces . · Includes surveys of other fractional-order spaces (Bessel potentials， Triebel-Lizorkin). · Develops the theory of Orlicz and Orlicz-Sobolev spaces and their imbeddings. Robert A. Adams is Professor Emeritus of Mathematics at The University of British Columbia， where he has taught since 1966. His research interests began in Partial Differential Equations and migrated to imbeddings of Sobolev Spaces. His latter work led to the first edition of this book. Later， he wrote a series of Calculus books， now in their fifth editions. He is now joined by John J. F. Fournier to prepare this second edition. John J. F. Fournier is Professor of Mathematics at The University of British Columbia， where he has taught since 1967. His research areas are Fourier Analysis and Function Spaces. He served as co-EDITOR: of the Canadian Mathematical Bulletin.