Duality for Orlicz spaces

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 consider associate spaces LΦ1 of Orlicz spaces LΦ. Using the Legendre transform of an Orlicz function Φ, we define the conjugate Orlicz function ψ just as the Legendre transform of Φ. We prove that the spaces LΦ1 and Lψ coincide as sets and ∥·∥Lψ ≤ ∥·∥LΦ1 ≤ 2∥ ∥Lψ. The duality between LΦ and Lψ is studied in detail.

Original languageEnglish
Title of host publicationDevelopments in Mathematics
PublisherSpringer New York LLC
Pages195-205
Number of pages11
DOIs
StatePublished - 1 Jan 2016

Publication series

NameDevelopments in Mathematics
Volume45
ISSN (Print)1389-2177

ASJC Scopus subject areas

  • Mathematics (all)

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