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An Introductory Course in Lebesgue Spaces

✍ Scribed by Rene Erlin Castillo, Humberto Rafeiro

Publisher
Springer
Year
2016
Tongue
English
Leaves
463
Series
CMS Books in Mathematics Ouvrages de mathématiques de la SMC
Edition
1st ed.
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Convex Functions and Inequalities....Pages 1-19
Front Matter....Pages 21-21
Lebesgue Sequence Spaces....Pages 23-42
Lebesgue Spaces....Pages 43-137
Distribution Function and Nonincreasing Rearrangement....Pages 139-182
Weak Lebesgue Spaces....Pages 183-214
Lorentz Spaces....Pages 215-268
Nonstandard Lebesgue Spaces....Pages 269-310
Front Matter....Pages 311-311
Interpolation of Operators....Pages 313-330
Maximal Operator....Pages 331-358
Integral Operators....Pages 359-382
Convolution and Potentials....Pages 383-417
Back Matter....Pages 419-461

✦ Subjects

Mathematics;Harmonic analysis;Functional analysis;Abstract Harmonic Analysis;Functional Analysis

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