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Analysis III

Spaces of Differentiable Functions

  • S. M. Nikol’skiĭ

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 26)

Table of contents

  1. Front Matter
    Pages i-3
  2. L. D. Kudryavtsev, S. M. Nikol’skiĭ
    Pages 1-140
  3. Back Matter
    Pages 213-224

About this book

Introduction

In the Part at hand the authors undertake to give a presentation of the historical development of the theory of imbedding of function spaces, of the internal as well as the externals motives which have stimulated it, and of the current state of art in the field, in particular, what regards the methods employed today. The impossibility to cover all the enormous material connected with these questions inevitably forced on us the necessity to restrict ourselves to a limited circle of ideas which are both fundamental and of principal interest. Of course, such a choice had to some extent have a subjective character, being in the first place dictated by the personal interests of the authors. Thus, the Part does not constitute a survey of all contemporary questions in the theory of imbedding of function spaces. Therefore also the bibliographical references given do not pretend to be exhaustive; we only list works mentioned in the text, and a more complete bibliography can be found in appropriate other monographs. O.V. Besov, v.1. Burenkov, P.1. Lizorkin and V.G. Maz'ya have graciously read the Part in manuscript form. All their critical remarks, for which the authors hereby express their sincere thanks, were taken account of in the final editing of the manuscript.

Keywords

Einbettungssätze Funktionenräume Sobolev Raum Sobolev Space Variationsrechnung calculus capacities function spaces imbedding theorems variational calculus

Editors and affiliations

  • S. M. Nikol’skiĭ
    • 1
  1. 1.Steklov Mathematical InstituteMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-09961-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08083-8
  • Online ISBN 978-3-662-09961-2
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site