Foundations of Symmetric Spaces of Measurable Functions: Lorentz, Marcinkiewicz and Orlicz Spaces

ISBN-13: 9783319427560 / Angielski / Twarda / 2016 / 259 str.

Ben-Zion A. Rubshtein; Genady Ya Grabarnik; Mustafa A. Muratov

Opis

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.

Recenzje

"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)

Spis treści

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.​

O autorze

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.