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CMS Books in Mathematics

An Introductory Course in Lebesgue Spaces

Authors: Castillo, Rene Erlin, Rafeiro, Humberto

  • 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
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Buy this book

eBook 55,92 €
price for Spain (gross)
  • ISBN 978-3-319-30034-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 69,67 €
price for Spain (gross)
  • ISBN 978-3-319-30032-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

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. 

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)


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Table of contents (11 chapters)

  • Convex Functions and Inequalities

    Castillo, René Erlín (et al.)

    Pages 1-19

    Preview Buy Chapter 30,19 €
  • Lebesgue Sequence Spaces

    Castillo, René Erlín (et al.)

    Pages 23-42

    Preview Buy Chapter 30,19 €
  • Lebesgue Spaces

    Castillo, René Erlín (et al.)

    Pages 43-137

    Preview Buy Chapter 30,19 €
  • Distribution Function and Nonincreasing Rearrangement

    Castillo, René Erlín (et al.)

    Pages 139-182

    Preview Buy Chapter 30,19 €
  • Weak Lebesgue Spaces

    Castillo, René Erlín (et al.)

    Pages 183-214

    Preview Buy Chapter 30,19 €

Buy this book

eBook 55,92 €
price for Spain (gross)
  • ISBN 978-3-319-30034-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 69,67 €
price for Spain (gross)
  • ISBN 978-3-319-30032-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
An Introductory Course in Lebesgue Spaces
Authors
Series Title
CMS Books in Mathematics
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-30034-4
DOI
10.1007/978-3-319-30034-4
Hardcover ISBN
978-3-319-30032-0
Series ISSN
1613-5237
Edition Number
1
Number of Pages
XII, 461
Number of Illustrations and Tables
14 b/w illustrations
Topics