The space L1∩L

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

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

The space L1 ∩ L, which we study in this chapter, consists of all bounded integrable functions equipped with the norm ∥·∥L1 ∩ L∞= max(∥·∥L1, ∥·∥L∞). We show that. (L1 ∩ L; ∥·∥L1 ∩ L∞) is a symmetric space and describe the closure L0 of L1 ∩ L in L. Given two equimeasurable functions f and g, we treat an approximation of g in the L1 ∩ L-norm by shifted functions f o θ, where θ is a measure-preserving transformation. Step functions and integrable simple functions are applied for this purpose.

Original languageEnglish
Title of host publicationDevelopments in Mathematics
PublisherSpringer New York LLC
Pages29-40
Number of pages12
DOIs
StatePublished - 1 Jan 2016

Publication series

NameDevelopments in Mathematics
Volume45
ISSN (Print)1389-2177

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