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  • © 2016

An Introductory Course in Lebesgue Spaces

  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xii
  2. Convex Functions and Inequalities

    • René Erlín Castillo, Humberto Rafeiro
    Pages 1-19
  3. Function Spaces

    1. Front Matter

      Pages 21-21
    2. Lebesgue Sequence Spaces

      • René Erlín Castillo, Humberto Rafeiro
      Pages 23-42
    3. Lebesgue Spaces

      • René Erlín Castillo, Humberto Rafeiro
      Pages 43-137
    4. Distribution Function and Nonincreasing Rearrangement

      • René Erlín Castillo, Humberto Rafeiro
      Pages 139-182
    5. Weak Lebesgue Spaces

      • René Erlín Castillo, Humberto Rafeiro
      Pages 183-214
    6. Lorentz Spaces

      • René Erlín Castillo, Humberto Rafeiro
      Pages 215-268
    7. Nonstandard Lebesgue Spaces

      • René Erlín Castillo, Humberto Rafeiro
      Pages 269-310
  4. A Concise Excursion into Harmonic Analysis

    1. Front Matter

      Pages 311-311
    2. Interpolation of Operators

      • René Erlín Castillo, Humberto Rafeiro
      Pages 313-330
    3. Maximal Operator

      • René Erlín Castillo, Humberto Rafeiro
      Pages 331-358
    4. Integral Operators

      • René Erlín Castillo, Humberto Rafeiro
      Pages 359-382
    5. Convolution and Potentials

      • René Erlín Castillo, Humberto Rafeiro
      Pages 383-417
  5. Back Matter

    Pages 419-461

About this book

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.

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)

Authors and Affiliations

  • Dept Math, Edificio Yu Takeuchi, Univ Nacional De Colombia, Bogota, Colombia

    Rene Erlin Castillo

  • Pontificia Universidad Javeriana, Bogota, Colombia

    Humberto Rafeiro

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

  • DOI: https://doi.org/10.1007/978-3-319-30034-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-30032-0Published: 06 July 2016

  • Softcover ISBN: 978-3-319-80709-6Published: 30 May 2018

  • eBook ISBN: 978-3-319-30034-4Published: 23 June 2016

  • Series ISSN: 1613-5237

  • Series E-ISSN: 2197-4152

  • Edition Number: 1

  • Number of Pages: XII, 461

  • Number of Illustrations: 14 b/w illustrations

  • Topics: Abstract Harmonic Analysis, Functional Analysis

Buy it now

Buying options

eBook USD 29.99 USD 59.99
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.99 USD 79.99
50% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 39.99 USD 79.99
50% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access