索伯列夫空間

前言

　　This monograph presents an introductory study of of the properties of certain Ba-nach spaces of weakly differentiable functions of several real variables that arise inconnection with numerous problems in the theory of partial differential equations，approximation theory， and many other areas of pure and applied mathematics.These spaces have become associated with the name of the late Russian mathe-matician S. L. Sobolev， although their origins predate his major contributions totheir development in the late 1930s.　　Even by 1975 when the first edition of this monograph was published， there wasa great deal of material on these spaces and their close relatives， though most of itwas available only in research papers published in a wide variety of journals. Themonograph was written to fill a perceived need for a single source where graduatestudents and researchers in a wide variety of disciplines could learn the essentialfeatures of Sobolev spaces that they needed for their particular applications. Noattempt was made even at that time for complete coverage. To quote from thePreface of the first edition.

內(nèi)容概要

　　This monograph presents an introductory study of of the properties of certain Ba-nach spaces of weakly differentiable functions of several real variables that arise inconnection with numerous problems in the theory of partial differential equations，approximation theory，and many other areas of pure and applied mathematics.These spaces have become associated with the name of the late Russian mathe-matician S. L. Sobolev，although their origins predate his major contributions totheir development in the late 1930s.

書籍目錄

Preface  Lisf of Spaces and Norms1. PRELIMINARIES  Notation  Topological Vector Spaces  Normed Spaces  Spaces of Continuous Functions  The Lebesgue Measure in Rn  The Lebesgue Integral  Distributions and Weak Derivatives2. THE LEBESGUE SPACES Lp(Ω)  Definition and Basic Properties　Completeness of Lp (Ω)　Approximation by Continuous Functions　Convolutions and Young's Theorem　Mollifiers and Approximation by Smooth Functions　Precompact Sets in Lp (Ω)　Uniform Convexity　 　The Normed Dual of LP(Ω)　Mixed-Norm Lp Spaces　The Marcinkiewicz Interpolation Theorem……

編輯推薦

　　The existing mathematical literature on Sobolev spaces and theirgeneralizations is vast， and it would be neither easy nor particularlydesirable to include everything that was known about such spacesbetween the covers of one book. An attempt has been made in thismonograph to present all the core material in sufficient generality tocover most applications， to give the reader an overview of the subjectthat is difficult to obtain by reading research papers， and finally ...to provide a ready reference for someone requiring a result aboutSobolev spaces for use in some application.

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