Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 10716 LNCS. 2018. P.. 210-220
On denseness of C0 ∞(Ω) and compactness in Lp(x)(Ω) for 0 < p(x) < 1
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. © 2018 Independent University of Moscow.
Authors
Bandaliev R.A. 1, 2 , Hasanov S.G. 1, 3
Journal
Publisher
Independent University of Moscow
Issue number
1
Language
English
Pages
1-13
State
Published
Link
Volume
18
Year
2018
Organizations
- 1 Institute of Mathematics and Mechanics of ANAS, Baku, AZ 1141, Azerbaijan
- 2 S. M. Nikolskii Institute of Mathematics at RUDN University, Moscow, 117198, Russian Federation
- 3 Gandja State University, Gandja, 117198, Azerbaijan
Keywords
Compactness; Denseness; Lp(x) spaces; Modular inequality; Potential type identity approximations
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