Separable Orlicz spaces

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

doi:10.1007/978-3-319-42758-4_14

Separable Orlicz spaces

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 conditions of separability for Orlicz spaces L_Φ. We consider Young classes Y_Φ, the subspaces H_Φ, and their embeddings H_Φ ⊆ Y_Φ ⊆ L_Φ. We show that the equality H_Φ= Y_Φ = L_Φ is equivalent to separability of L_Φ. This and other equivalents of separability studied earlier in Chapters 6 and 7 can be expressed in term of an Orlicz function Φ. The (Δ₂) condition is described to this end in detail.

Original language	English
Title of host publication	Developments in Mathematics
Publisher	Springer New York LLC
Pages	183-193
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-319-42758-4_14
State	Published - 1 Jan 2016

Publication series

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

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10.1007/978-3-319-42758-4_14

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AU - Grabarnik, Genady Ya

AU - Muratov, Mustafa A.

AU - Pashkova, Yulia S.

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N2 - In this chapter, we study conditions of separability for Orlicz spaces LΦ. We consider Young classes YΦ, the subspaces HΦ, and their embeddings HΦ ⊆ YΦ ⊆ LΦ. We show that the equality HΦ= YΦ = LΦ is equivalent to separability of LΦ. This and other equivalents of separability studied earlier in Chapters 6 and 7 can be expressed in term of an Orlicz function Φ. The (Δ2) condition is described to this end in detail.

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Separable Orlicz spaces

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