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

Mathematics (all)

Access to Document

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

Cite this

@inbook{da12d829ea8f490d8b59237e667af9e0,

title = "Spaces Lp, 1≤ p≤∞",

abstract = "In this chapter we study the class of Lp spaces, 1 ≤ p≤∞, which is one of the most important classes of symmetric spaces. We begin with the H{\"o}lder and Minkowski inequalities and prove that Lp is a symmetric space for all 1 ≤ p ≤ ∞. In the case 1 ≤ p < ∞, we show that Lp is separable and describe its dual.",

author = "Rubshtein, {Ben Zion A.} and Grabarnik, {Genady Ya} and Muratov, {Mustafa A.} and Pashkova, {Yulia S.}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",

year = "2016",

month = jan,

day = "1",

doi = "10.1007/978-3-319-42758-4_2",

language = "English",

series = "Developments in Mathematics",

publisher = "Springer New York LLC",

pages = "17--27",

booktitle = "Developments in Mathematics",

}

TY - CHAP

T1 - Spaces Lp, 1≤ p≤∞

AU - Rubshtein, Ben Zion A.

AU - Grabarnik, Genady Ya

AU - Muratov, Mustafa A.

AU - Pashkova, Yulia S.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this chapter we study the class of Lp 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 Lp is a symmetric space for all 1 ≤ p ≤ ∞. In the case 1 ≤ p < ∞, we show that Lp is separable and describe its dual.

AB - In this chapter we study the class of Lp 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 Lp is a symmetric space for all 1 ≤ p ≤ ∞. In the case 1 ≤ p < ∞, we show that Lp is separable and describe its dual.

UR - http://www.scopus.com/inward/record.url?scp=85006263037&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42758-4_2

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

M3 - Chapter

AN - SCOPUS:85006263037

T3 - Developments in Mathematics

SP - 17

EP - 27

BT - Developments in Mathematics

PB - Springer New York LLC

ER -