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

• Main Authors: Rubshtein, Ben-Zion A. (Author), Grabarnik, Genady Ya (Author), Muratov, Mustafa A. (Author), Pashkova, Yulia S. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: Developments in Mathematics, 45
• Subjects: Mathematics.; 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).

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 research...

Table of 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.