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  • © 2016

Foundations of Symmetric Spaces of Measurable Functions

Lorentz, Marcinkiewicz and Orlicz Spaces

  • Includes applications of symmetric spaces to Ergodic theory
  • Contains a detailed study of Lorentz, Marcinkiewicz and Orlicz spaces
  • Provides results with applications in functional analysis?
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (17 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-3
    2. Definition of Symmetric Spaces

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 5-15
    3. Spaces L p ,  1 ≤ p ≤ 

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 17-27
    4. The Space L 1L

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 29-40
    5. The Space L 1 +L

      • 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. Embeddings L1 ∩ L∞ ⊆ X ⊆ L1 + L∞ ⊆ L0

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 59-70
    3. Embeddings. Minimality and Separability. Property (A)

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 71-81
    4. Associate Spaces

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 83-93
    5. Maximality. Properties (B) and (C)

      • 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. Lorentz Spaces

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 115-125
    3. Quasiconcave Functions

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 127-137
    4. Marcinkiewicz Spaces

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 139-150
    5. Embedding \(\varLambda _{\widetilde{V }}^{0}\) ⊆ X ⊆ MV*

      • 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. Definition and Examples of Orlicz Spaces

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 171-182
    3. Separable Orlicz Spaces

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 183-193
    4. Duality for Orlicz Spaces

      • Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova
      Pages 195-205

About this book

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 materialto assist students with independent work. 

Reviews

“This book represents a consistent reference on the basic theory of symmetric spaces of measurable functions also known as rearrangement invariant function spaces. … The text contains many illustrations in order to clarify concepts and make the theory more comprehensive and understandable. … The book is structured in such a way that it should correspond to a one-semester special course of lectures … .” (Santiago Boza, zbMATH 1361.42001, 2017)

Authors and Affiliations

  • Mathematics, Ben Gurion University of the Negev, Be’er Sheva, Israel

    Ben-Zion A. Rubshtein

  • Mathematics and Computer Science, St. John’s University, New York, USA

    Genady Ya. Grabarnik

  • Mathematics and Computer Sciences, V.I. Vernadsky Crimean Federal University, Simferopol, Russia

    Mustafa A. Muratov, Yulia S. Pashkova

About the authors

Ben-Zion A. Rubshtein is a Professor in the Department of Mathematics at Ben Gurion University. His research interests are ergodic theory and probability.

Genady Ya. Grabarnik is an Associate Professor in the Mathematics and Computer Science Department at St. John's University.  His research interest is in functional analysis.

Mustafa A. Muratov is a Professor in the Mathematics and Computer Science Department at Taurida National University. His research interest is in functional analysis.

Yulia S. Pashkova is a Professor in the Mathematics and Computer Science Department at Taurida National University. Her research interest is in dynamical systems and ergodic theory. 

Bibliographic Information

Buy it now

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 79.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access