Spaces Lp, 1≤ p≤∞

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

doi:10.1007/978-3-319-42758-4_2

Spaces L_p, 1≤ p≤∞

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 the class of L_p spaces, 1 ≤ p≤∞, which is one of the most important classes of symmetric spaces. We begin with the Hölder and Minkowski inequalities and prove that L_p is a symmetric space for all 1 ≤ p ≤ ∞. In the case 1 ≤ p < ∞, we show that L_p is separable and describe its dual.

Original language	English
Title of host publication	Developments in Mathematics
Publisher	Springer New York LLC
Pages	17-27
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-319-42758-4_2
State	Published - 1 Jan 2016

Publication series

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

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-42758-4_2

Cite this

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