The space L1 + L∞

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

doi:10.1007/978-3-319-42758-4_4

The space L₁ + L_∞

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 study the sum L₁ + L_∞ of the spaces L₁ and L_∞. We show that L₁ + L_∞ equipped with a natural norm ∥·∥_{L₁+ L∞} is a symmetric space. The norm ∥·∥_{L₁+ L∞} can be written in the form ∫₀¹f* dm using the maximal property of decreasing rearrangements f*. We also describe embeddings of L₁ and L_∞ into L₁ + L_∞ and the closure R₀ of L₁ in L₁ + L_∞.

Original language	English
Title of host publication	Developments in Mathematics
Publisher	Springer New York LLC
Pages	41-56
Number of pages	16
DOIs	https://doi.org/10.1007/978-3-319-42758-4_4
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_4

Cite this

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AB - In this chapter, we study the sum L1 + L∞ of the spaces L1 and L∞. We show that L1 + L∞ equipped with a natural norm ∥·∥L1+ L∞ is a symmetric space. The norm ∥·∥L1+ L∞ can be written in the form ∫01f* dm using the maximal property of decreasing rearrangements f*. We also describe embeddings of L1 and L∞ into L1 + L∞ and the closure R0 of L1 in L1 + L∞.

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