Foundations of Symmetric Spaces of Measurable Functions : Lorentz, Marcinkiewicz and Orlicz Spaces / by Ben-Zion A. Rubshtein, Genady Ya. Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova.

Format:

Book

Author/Creator:

Rubshtein, Ben-Zion A., lat, Author.

Grabarnik, Genady Ya., Author.

Muratov, Mustafa A., Author.

Pashkova, Yulia S., Author.

Series:

Developments in Mathematics, 1389-2177 ; 45

Language:

English

Subjects (All):

Functional analysis.

Measure theory.

Functions of complex variables.

Manifolds (Mathematics).

Complex manifolds.

Functional Analysis.

Measure and Integration.

Several Complex Variables and Analytic Spaces.

Manifolds and Cell Complexes (incl. Diff.Topology).

Local Subjects:

Functional Analysis.

Measure and Integration.

Several Complex Variables and Analytic Spaces.

Manifolds and Cell Complexes (incl. Diff.Topology).

Physical Description:

1 online resource (XVII, 259 p. 90 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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.

Contents:

1.Definition of the symmetric space

2.Spaces Lp

3.The space L1 ∩ L ∞

4. The space L1+L∞

5. The embedding L1 ∩L∞ ⊆ X ⊆ L1+L∞ ⊆ L0

6. Embeddings, Minimality and Separability: The property

7. Associated Spaces

8. Maximality Properties (B) and (C)

9. Lorentz spaces

10. Quasi-concave functions

11. Marcinkiewicz spaces

12. Embedding

13. Definition and examples of Orlicz spaces

14. Separable Orlicz Spaces

15. Duality for Orlicz spaces

16. Comparison of Orlicz spaces

17. The intersection and sum of Orlicz spaces.– Complements

Index.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-42758-X

OCLC:

967712919