Series 
Developments in mathematics, 13892177 ; volume 45 

Developments in mathematics ;
v. 45.

Subject 
Symmetric spaces.

Alt Name 
Rubshtein, BenZion A.


Grabarnik, Genady Ya.


Muratov, Mustafa A.


Pashkova, Yulia S.

Description 
1 online resource. 
Bibliography Note 
Includes bibliographical references and index. 
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. Quasiconcave 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. 
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 selfcontained text is presented in four parts totaling seventeen chapters to correspond with a onesemester 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. 
Note 
Print version record. 
ISBN 
9783319427584 (electronic bk.) 

331942758X (electronic bk.) 

9783319427560 (print) 

3319427563 (print) 
ISBN/ISSN 
10.1007/9783319427584 
OCLC # 
967712919 
Additional Format 
Print version: Foundations of symmetric spaces of measurable functions. Cham, Switzerland : Springer, 2016 9783319427560 3319427563 (OCoLC)952384188 
