Embeddings L1 ∩ L∞ ⊆ x ⊆ L1 + L∞ ⊆ L0

Ben Zion A. Rubshtein; Genady Ya Grabarnik; Mustafa A. Muratov; Yulia S. Pashkova

doi:10.1007/978-3-319-42758-4_5

Embeddings L₁ ∩ L_∞ ⊆ x ⊆ L₁ + L_∞ ⊆ L₀

Ben Zion A. Rubshtein, Genady Ya Grabarnik, Mustafa A. Muratov, Yulia S. Pashkova

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

In this chapter, we prove the main embedding theorem for symmetric spaces. The theorem asserts that for every symmetric space X, there are continuous embeddings L₁ ∩ L_∞ ⊆ X ⊆ L₁ + L_∞ and inequalities 2∥·∥_L₁∩L∞.≥(φ_X)^-1(1)×∥·∥X≥ ≥ ∥·∥_L1+L∞: The space L₀ of all measurable functions and the embedding L₁ + L_∞ ⊂ L₀ are also considered.

Original language	English
Title of host publication	Developments in Mathematics
Publisher	Springer New York LLC
Pages	59-70
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-319-42758-4_5
State	Published - 1 Jan 2016

Publication series

Name	Developments in Mathematics
Volume	45
ISSN (Print)	1389-2177

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-42758-4_5

Cite this

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abstract = "In this chapter, we prove the main embedding theorem for symmetric spaces. The theorem asserts that for every symmetric space X, there are continuous embeddings L1 ∩ L∞ ⊆ X ⊆ L1 + L∞ and inequalities 2∥·∥L1∩L∞.≥(φX)-1(1)×∥·∥X≥ ≥ ∥·∥L1+L∞: The space L0 of all measurable functions and the embedding L1 + L∞ ⊂ L0 are also considered.",

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AU - Muratov, Mustafa A.

AU - Pashkova, Yulia S.

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