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

Parametric Marcinkiewicz integral operator on generalized Orlicz-Morrey spaces

In this paper we study the boundedness of the parametric Marcinkiewicz integral operator µ? ? on generalized Orlicz-Morrey spaces M?,?;'. We find the sufficient conditions on the pair (?1; ?'2;?) which ensure the boundedness of the operators µ?,? from one generalized Orlicz-Morrey space M?;?1 to another M?,?2. As an application of the above result, the boundedness of the Marcinkiewicz operator associated with Schrödinger operator µL j on generalized Orlicz-Morrey spaces is also obtained. © 2016, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.FEF.A3.16.011 --The research of F. Deringoz was partially supported by the grant of Ahi Evran University Scientific Research Project (FEF.A3.16.011). -

ON DENSENESS OF C-0(infinity)(Omega) AND COMPACTNESS IN Lp(x)(Omega) FOR 0 < p(x) < 1

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

ON DENSENESS OF C-0(infinity)(Omega) AND COMPACTNESS IN Lp(x)(Omega) FOR 0 < p(x) < 1

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

On denseness of C0 ∞(Ω) and compactness in Lp(x)(Ω) for 0 &lt; p(x) &lt; 1

The main goal of this paper is to prove the denseness of C0 ∞(Ω) in Lp(x) (Ω) for 0 &lt; p(x) &lt; 1. We construct a family of potential type identity approximations and prove a modular inequality in Lp(x) (Ω) for 0 &lt; p(x) &lt; 1. As an application we prove an analogue of the Kolmogorov–Riesz type compactness theorem in Lp(x) (Ω) for 0 &lt; p(x) &lt; 1. © 2018 Independent University of Moscow

Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces

We consider generalized Morrey spaces M p(·),?(?) with variable exponent p(x) and a general function ?(x,r) defining the Morrey-type norm. In case of bounded sets ? ? Rn we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev-Adams type M p(·),?(?) › Mq(·),? (?)-theorem for the potential operators I?(·), also of variable order. The conditions for the boundedness are given it terms of Zygmund-type integral inequalities on ?(x, r), which do not assume any assumption on monotonicity of ?(x, r) in r

Коммутаторы дробного максимального оператора на пространствах Орлича

In the present paper, we give necessary and sufficient conditions for the boundedness of commutators of fractional maximal operator on Orlicz spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators.В этой статье мы приводим необходимые и достаточные условия для ограниченности коммутаторов дробного максимального оператора на пространствах Орлича. Основное достижение по сравнению с существующими результатами заключается в том, что нам удалось получить условия для ограниченности не в интегральных терминах, а в менее ограничивающих терминах супремальных операторов.Библиография: 14 названий

Commutators of fractional maximal operator on generalized Orlicz–Morrey spaces

In the present paper, we shall give necessary and sufficient conditions for the Spanne and Adams type boundedness of the commutators of fractional maximal operator on generalized Orlicz–Morrey spaces, respectively. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators. © 2017, Springer International Publishing

Boundedness of maximal, potential type, and singular integral operators in the generalized variable exponent Morrey type spaces

We consider generalized Morrey type spaces Mp(·), ?(·), ?(·) (?)with variable exponents p(x), ?(r) and a general function ?(x, r) defining a Morrey type norm. In the case of bounded sets ? ? Rn, we prove the boundedness of the Hardy-Littlewood maximal operator and Calderón-Zygmund singular integral operators with standard kernel. We prove a Sobolev-Adams type embedding theorem Mp(·), ?1(·), ?1(·) (?) › Mp(·), ?2(·), ?2(·) (?) for the potential type operator I?(·) of variable order. In all the cases, we do not impose any monotonicity type conditions on ?(x, r) with respect to r. Bibliography: 40 titles. © 2010 Springer Science+Business Media, Inc.Firat University Scientific Research Projects Management Unit 1001-2010-2-53666 British Association for Psychopharmacology --The research of V. S. Guliyev and S. G. Samko was partially supported by the scientific and technological research council of Turkey (grant No. 1001-2010-2-53666 (TUBITAK Project)). The research of V. S. Guliyev was supported by 2010-Ahi Evran University Scientific Research Projects (BAP). -

Riesz potential and its commutators on Orlicz spaces

In the present paper, we shall give necessary and sufficient conditions for the strong and weak boundedness of the Riesz potential operator Iα on Orlicz spaces. Cianchi (J. Lond. Math. Soc. 60(1):247-286, 2011) found necessary and sufficient conditions on general Young functions Φ and Ψ ensuring that this operator is of weak or strong type from LΦ into LΨ. Our characterizations for the boundedness of the above-mentioned operator are different from the ones in (Cianchi in J. Lond. Math. Soc. 60(1):247-286, 2011). As an application of these results, we consider the boundedness of the commutators of Riesz potential operator [ b, Iα] on Orlicz spaces when b belongs to the BMO and Lipschitz spaces, respectively. © 2017, The Author(s)