Embedding (Forumula presented)

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 prove the embedding theorem for classes of symmetric spaces having the same fundamental functions. The embedding theorem asserts that for every symmetric space X with a given fundamental function V = φX, there are continuous embeddings (Formula Presented). This means that the minimal part (Formula Presented) of the Lorentz space (Formula Presented) is the smallest symmetric space whose (concave) fundamental function Ṽ is equivalent to V, while the Marcinkiewicz space MV* is the largest symmetric space X with φX = φMV*= V. The renorming theorem and other consequences of the embedding theorem are considered.

Original languageEnglish
Title of host publicationDevelopments in Mathematics
PublisherSpringer New York LLC
Pages151-167
Number of pages17
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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