Geodesic
Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 365-385

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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 $1$ 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.
DOI : 10.1007/s10587-014-0107-8
Classification : 42B20, 42B25, 42B35
Keywords: generalized weighted Morrey space; sublinear operator; commutator; BMO space; maximal operator; Calderón-Zygmund operator 
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     author = {Guliyev, Vagif Sabir and Karaman, Turhan and Mustafayev, Rza Chingiz and \c{S}erbet\c{c}i, Ayhan},
     title = {Commutators of sublinear operators generated by {Calder\'on-Zygmund} operator on generalized weighted {Morrey} spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {365--385},
     publisher = {mathdoc},
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Guliyev, Vagif Sabir; Karaman, Turhan; Mustafayev, Rza Chingiz; Şerbetçi, Ayhan. Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 2, pp. 365-385. doi: 10.1007/s10587-014-0107-8

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