Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

Title:

Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces

Creator:

Guliyev, Vagif Sabir, Karaman, Turhan, Mustafayev, Rza Chingiz, and Şerbetçi, Ayhan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5f4bdaf5-8d14-4ac9-8b5b-d1e1b6ec21b9
uuid:5f4bdaf5-8d14-4ac9-8b5b-d1e1b6ec21b9

Subject:

generalized weighted Morrey space, sublinear operator;, commutator, BMO space, maximal operator, and Calderón-Zygmund operator

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

In this paper, the boundedness of a large class of sublinear commutator operators $T_{b}$ generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces $M_{p,\varphi }(w)$ with the weight function $w$ belonging to Muckenhoupt's class $A_{p}$ is studied. When $1<p<\infty $ and $b \in {\rm BMO}$, sufficient conditions on the pair $(\varphi _1,\varphi _2)$ which ensure the boundedness of the operator $T_{b}$ from $M_{p,\varphi _1}(w)$ to $M_{p,\varphi _2}(w)$ are found. In all cases the conditions for the boundedness of $T_{b}$ are given in terms of Zygmund-type integral inequalities on $(\varphi _1,\varphi _2)$, which do not require any assumption on monotonicity of $\varphi _1(x,r)$, $\varphi _2(x,r)$ in $r$. Then these results are applied to several particular operators such as the pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

365-385

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:2

Harvested from:

CDK

Metadata only:

false