The structure of functions = 函数结构 /

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作   者:Hans Triebel.

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ISBN:9787510027413

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简介

  this book is mainly based on the results of the author and his co-workers ob-tained in the last few years. we tried to present the material in such a way that the main ideas can be understood independently of the existing literature. on the other hand, after proving in chapter i that the function spaces introduced via quarkonial decompositions coincide with the well-established spaces b8pq and fspq we feel free to use known results about these spaces, especially when we have nothing new to say about the assertions used. a reader who is mostly interested in the material presented in one of the chapters ii, iii, or iv, which are largely independent of each other, may skip chapter i, at the first glance.but most of the related proofs in these chapters depend substantially on the theory developed in the first chapter.   it is a pleasure to acknowledge the great help i have received from my col-laborators in jena, in particular dorothee haroske and winfried sickel, who made valuable suggestions which have been incorporated in the text. i am especially indebted to dorothee haroske for producing all the figures in this book. last, but not least, i wish to thank my friend and colleague david edmunds in brighton who looked through the whole manuscript and offered many comments.

目录

  Preface
  Ⅰ Decompositions of Functions
   1 Introduction, heuristics, and preliminaries
   2 Spaces on Rn: the regular case
   3 Spaces on Rn: the general case
   4 An application: the Fubini property
   5 Spaces on domains: localization and Hardy inequalities
   6 Spaces on domains: decompositions
   7 Spaces on manifolds
   8 Taylor expansions of distributions
   9 Traces on sets, related function spaces and their decompositions
  Ⅱ Sharp Inequalities
   10 Introduction: Outline of methods and results
   11 Classical inequalities
   12 Envelopes
   13 The critical case
   14 The super-critical case
   15 The sub-critical case
   16 Hardy inequalities
   17 Complements
  Ⅲ Fractal Elliptic Operators
   18 Introduction
   19 Spectral theory for the fractal Laplacian
   20 The fractal Dirichlet problem
   21 Spectral theory on manifolds
   22 Isotropic fractals and related function spaces
   23 Isotropic fractal drums
  Ⅳ Truncations and Semi-linear Equations
   24 Introduction
   25 Truncations
   26 The Q-operator
   27 Semi-linear equations; the Q-method
  References
  Symbols
  Index
  

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