An Introductory Course in Lebesgue Spaces
Authors: Castillo, Rene Erlin, Rafeiro, Humberto
Free Preview- 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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- About this Textbook
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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
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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
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“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)
- Video
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- Table of contents (11 chapters)
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Convex Functions and Inequalities
Pages 1-19
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Lebesgue Sequence Spaces
Pages 23-42
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Lebesgue Spaces
Pages 43-137
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Distribution Function and Nonincreasing Rearrangement
Pages 139-182
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Weak Lebesgue Spaces
Pages 183-214
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Table of contents (11 chapters)
- Download Preface 1 PDF (56.2 KB)
- Download Sample pages 1 PDF (341 KB)
- Download Table of contents PDF (89.2 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- An Introductory Course in Lebesgue Spaces
- Authors
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- Rene Erlin Castillo
- Humberto Rafeiro
- 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
- Softcover ISBN
- 978-3-319-80709-6
- Series ISSN
- 1613-5237
- Edition Number
- 1
- Number of Pages
- XII, 461
- Number of Illustrations
- 14 b/w illustrations
- Topics
