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

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 languageEnglish
Title of host publicationDevelopments in Mathematics
PublisherSpringer New York LLC
Pages41-56
Number of pages16
DOIs
StatePublished - 1 Jan 2016

Publication series

NameDevelopments in Mathematics
Volume45
ISSN (Print)1389-2177

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