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Moscow Mathematical Journal

Volume 18, Issue 1, January–March 2018  pp. 1–13.

On Denseness of C0(Ω) and Compactness in Lp(x)(Ω) for 0<p(x)<1

Authors:  R. A. Bandaliev (1) and S. G. Hasanov (2)
Author institution:(1) Institute of Mathematics and Mechanics of ANAS, AZ 1141 Baku, Azerbaijan;
S.M. Nikolskii Institute of Mathematics at RUDN University, 117198 Moscow, Russia
(2) Institute of Mathematics and Mechanics of ANAS, AZ 1141 Baku, Azerbaijan;
Gandja State University, Gandja, Azerbaijan


Summary: 

The main goal of this paper is to prove the denseness of C0(Ω) in Lp(x)(Ω) for 0<p(x)<1. We construct a family of potential type identity approximations and prove a modular inequality in Lp(x)(Ω) for 0<p(x)<1. As an application we prove an analogue of the Kolmogorov–Riesz type compactness theorem in Lp(x)(Ω) for 0<p(x)<1.

2010 Math. Subj. Class. Primary: 46E30, 46E35; Secondary: 26D15.



Keywords: Lp(x) spaces, denseness, potential type identity approximations, modular inequality, compactness.

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