Function Spaces, 1: Volume 1

Luboš Pick; Alois Kufner; Oldřich John; Svatopluk Fucík

Published by De Gruyter 2013

Function Spaces, 1

Luboš Pick , Alois Kufner , Oldřich John and Svatopluk Fucík

Volume 14/1 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110250428

Overview
Contents

About this book

This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses.

This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.

Author / Editor information

Luboš Pick, Charles University, Prague, Czech Republic; Alois Kufner, The Academy of Sciences of the Czech Republic, Prague, Czech Republic; Oldřich John, Charles University, Prague, Czech Republic; Svatopluk Fučík †.

Reviews

"Das Buch stellt dadurch eine nützliche Informationsquelle (ergänzt durch ein umfangreiches Literaturverzeichnis)dar, in einem nicht besonders übersichtlichen Teilgebiet."
V. Losert in: Monatsh Math 186 (2018), 561–564

Supplementary Materials

Contents

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	xi
Chapter 1. Preliminaries Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. Spaces of smooth functions Requires Authentication Unlicensed Licensed Download PDF	38
Chapter 3. Lebesgue spaces Requires Authentication Unlicensed Licensed Download PDF	62
Chapter 4. Orlicz spaces Requires Authentication Unlicensed Licensed Download PDF	108
Chapter 5. Morrey and Campanato spaces Requires Authentication Unlicensed Licensed Download PDF	173
Chapter 6. Banach function spaces Requires Authentication Unlicensed Licensed Download PDF	203
Chapter 7. Rearrangement-invariant spaces Requires Authentication Unlicensed Licensed Download PDF	237
Chapter 8. Lorentz spaces Requires Authentication Unlicensed Licensed Download PDF	301
Chapter 9. Generalized Lorentz–Zygmund spaces Requires Authentication Unlicensed Licensed Download PDF	313
Chapter 10. Classical Lorentz spaces Requires Authentication Unlicensed Licensed Download PDF	375
Chapter 11. Variable-exponent Lebesgue spaces Requires Authentication Unlicensed Licensed Download PDF	437
Bibliography Requires Authentication Unlicensed Licensed Download PDF	459
Index Requires Authentication Unlicensed Licensed Download PDF	472

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 2nd rev. and ext. ed.
Audience: Researchers and graduate students in mathematical analysis.
Pages
- Front matter: 15
- Main content: 479
Illustrations
- Illustrations: 5
Keywords: Mathematics; Function space; Lebesgue; Banach; Lorentz; Orlicz; Sobolev

eBook

Published: December 19, 2012
ISBN: 9783110250428

Hardcover

Published: December 13, 2012
ISBN: 9783110250411