Advertisement

© 2016

An Introductory Course in Lebesgue Spaces

Benefits

  • Introduces reader to recent topics in spaces of measurable functions

  • Includes section of problems at the end of each chapter ?

  • Content allows for use with mixed-level classes

  • Includes non-standard function spaces, viz. variable exponent Lebesgue spaces and grand Lebesgue spaces

Textbook

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

  1. 1.Dept Math, Edificio Yu TakeuchiUniv Nacional De ColombiaBogotaColombia
  2. 2.Pontificia Universidad JaverianaBogotaColombia

About the authors

René Erlín Castillo obtained his PhD from Ohio University. He has been professor in Universidad de Oriente, Venezuela, Visiting Professor in Ohio University and nowadays he is a professor in the Universidad Nacional de Colombia. His research, spread across  around 50 papers, is done mainly in functional analysis, real analysis, complex analysis, harmonic analysis, operator theory, potential theory and partial Differential Equations. He has authored a book and a textbook both in Spanish.

 

Humberto Rafeiro received his PhD from Algarve University, Portugal and did postdoctoral work in the research group Centro de Análise Funcional e Aplicações in the Instituto Superior Técnico, Universidade de Lisboa, Portugal. Nowadays he is a professor in the Pontifical Universidad Javeriana. His research interests range from harmonic analysis, function spaces, operator theory in non-standard function spaces, potential type operators, hypersingular integrals and fractional calculus, having published near 40 papers on these subjects. He has co-authored a textbook in Spanish. 

Bibliographic information

  • Book Title An Introductory Course in Lebesgue Spaces
  • Authors Rene Erlin Castillo
    Humberto Rafeiro
  • Series Title CMS Books in Mathematics
  • Series Abbreviated Title CMS Books in Mathematics
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-30032-0
  • Softcover ISBN 978-3-319-80709-6
  • eBook ISBN 978-3-319-30034-4
  • Series ISSN 1613-5237
  • Series E-ISSN 2197-4152
  • Edition Number 1
  • Number of Pages XII, 461
  • Number of Illustrations 14 b/w illustrations, 0 illustrations in colour
  • Topics Abstract Harmonic Analysis
    Functional Analysis
  • Buy this book on publisher's site

Reviews

“The book under review is dedicated solely to Lebesgue spaces and their direct derivatives … . The book may be recommended to graduate students and non-specialists in the area of function spaces. … Each chapter is concluded with an extensive list of problems and short bibliographic notes. … The book ends with a list of 86 references and with symbol and subject indices.” (Alexei Yu. Karlovich, zbMATH 1352.46003, 2017)