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Foundations of Symmetric Spaces of Measurable Functions

Lorentz, Marcinkiewicz and Orlicz Spaces

  • Ben-Zion A. Rubshtein
  • Genady Ya. Grabarnik
  • Mustafa A. Muratov
  • Yulia S. Pashkova

Part of the Developments in Mathematics book series (DEVM, volume 45)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Symmetric Spaces: The Spaces Lp,L1 ∩ L∞, L1 + L∞

    1. Front Matter
      Pages 1-3
    2. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 5-15
    3. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 17-27
    4. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 29-40
    5. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 41-56
  3. Symmetric Spaces: The Embedding Theorem. Properties (A), (B), (C)

    1. Front Matter
      Pages 57-58
    2. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 59-70
    3. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 71-81
    4. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 83-93
    5. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 95-110
  4. Lorentz and Marcinkiewicz Spaces

    1. Front Matter
      Pages 111-113
    2. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 115-125
    3. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 127-137
    4. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 139-150
    5. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 151-167
  5. Orlicz Spaces

    1. Front Matter
      Pages 169-170
    2. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 171-182
    3. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 183-193
    4. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 195-205
    5. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 207-216
    6. Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 217-235
  6. Back Matter
    Pages 237-259

About this book

Introduction

Key definitions and results in symmetric spaces, particularly Lp, Lorentz, Marcinkiewicz and Orlicz spaces are emphasized in this textbook. A comprehensive overview of the Lorentz, Marcinkiewicz and Orlicz spaces is presented based on concepts and results of symmetric spaces. Scientists and researchers will find the application of linear operators, ergodic theory, harmonic analysis and mathematical physics noteworthy and useful.

This book is intended for graduate students and researchers in mathematics and may be used as a general reference for the theory of functions, measure theory, and functional analysis. This self-contained text is presented in four parts totaling seventeen chapters to correspond with a one-semester lecture course. Each of the four parts begins with an overview and is subsequently divided into chapters, each of which concludes with exercises and notes. A chapter called “Complements” is included at the end of the text as supplementary material to assist students with independent work.

Keywords

Lorentz spaces Marcinkiewicz spaces Orlicz spaces Quasi-concave functions Symmetric spaces Theorem embedding Quasi-convex functions Zygmund’s classes Orlicz-Lorentz spaces Ergodic theory measure functions

Authors and affiliations

  • Ben-Zion A. Rubshtein
    • 1
  • Genady Ya. Grabarnik
    • 2
  • Mustafa A. Muratov
    • 3
  • Yulia S. Pashkova
    • 4
  1. 1.MathematicsBen Gurion University of the NegevBe’er ShevaIsrael
  2. 2.Mathematics and Computer ScienceSt. John’s UniversityNew YorkUSA
  3. 3.Mathematics and Computer SciencesV.I. Vernadsky Crimean Federal UniversitySimferopolRussia
  4. 4.Mathematics and Computer SciencesV.I. Vernadsky Crimean Federal UniversitySimferopolRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42758-4
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-42756-0
  • Online ISBN 978-3-319-42758-4
  • Series Print ISSN 1389-2177
  • Series Online ISSN 2197-795X
  • Buy this book on publisher's site