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An Introductory Course in Lebesgue Spaces

  • Rene Erlin Castillo
  • Humberto Rafeiro

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. René Erlín Castillo, Humberto Rafeiro
    Pages 1-19
  3. Function Spaces

    1. Front Matter
      Pages 21-21
    2. René Erlín Castillo, Humberto Rafeiro
      Pages 23-42
    3. René Erlín Castillo, Humberto Rafeiro
      Pages 43-137
    4. René Erlín Castillo, Humberto Rafeiro
      Pages 139-182
    5. René Erlín Castillo, Humberto Rafeiro
      Pages 183-214
    6. René Erlín Castillo, Humberto Rafeiro
      Pages 215-268
    7. René Erlín Castillo, Humberto Rafeiro
      Pages 269-310
  4. A Concise Excursion into Harmonic Analysis

    1. Front Matter
      Pages 311-311
    2. René Erlín Castillo, Humberto Rafeiro
      Pages 313-330
    3. René Erlín Castillo, Humberto Rafeiro
      Pages 331-358
    4. René Erlín Castillo, Humberto Rafeiro
      Pages 359-382
    5. René Erlín Castillo, Humberto Rafeiro
      Pages 383-417
  5. Back Matter
    Pages 419-461

About this book

Introduction

This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement. Moreover, it also deals with weak, Lorentz and the more recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. The book also touches on basic harmonic analysis in the aforementioned spaces. An appendix is given at the end of the book giving it a self-contained character. This work is ideal for teachers, graduate students and researchers.

Keywords

Convex functions Lebesgue spaces Lorentz spaces Variable exponent Lebesgue spaces Grand Lebesgue spaces Interpolation of operators Maximal operator

Authors and affiliations

  • Rene Erlin Castillo
    • 1
  • Humberto Rafeiro
    • 2
  1. 1.Dept Math, Edificio Yu TakeuchiUniv Nacional De ColombiaBogotaColombia
  2. 2.Pontificia Universidad JaverianaBogotaColombia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-30034-4
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-30032-0
  • Online ISBN 978-3-319-30034-4
  • Series Print ISSN 1613-5237
  • Series Online ISSN 2197-4152
  • Buy this book on publisher's site