Abstract
In this paper, we acquire the boundedness of commutators generated by multilinear Calderón-Zygmund operator and BMO functions on products of weighted Herz-Morrey spaces with variable exponents.
Highlights
The space of all Schwartz functions on Rn was denoted by SðRnÞ, and the space of all tempered distributions on Rn was denoted by S ′ðRnÞ
The space of compactly supported bounded functions denoted by L∞ C ðRnÞ, and the support set of function f was denoted by supp ðf Þ
On the m-fold of the Schwartz function space SðRnÞ, we set T as an m -linear operator originally defined and m ≥ 2, and its value belongs to S ′ðRnÞ: T : SðRnÞ × SðRnÞ × ⋯ × SðRnÞ ⟶ S ′ðRnÞ: ð1Þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl {zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl }
Summary
The space of all Schwartz functions on Rn was denoted by SðRnÞ, and the space of all tempered distributions on Rn was denoted by S ′ðRnÞ. On the m-fold of the Schwartz function space SðRnÞ, we set T as an m -linear operator originally defined and m ≥ 2, and its value belongs to S ′ðRnÞ:. Journal of Function Spaces oscillation if kbk∗ < ∞: Denote by BMOðRnÞ the set of all bounded mean oscillation functions on Rn: our method suits any multilinear operator, only the bilinear Calderón-Zygmund operator will be considered here for the sake of simplicity. Tang et al [3] obtained the boundedness of a commutator generated by the multilinear Calderón-Zygmund operator and BMO functions in Herz-Morrey spaces with variable exponents. Motivated by the mentioned works, we will consider the boundedness of commutators generated by multilinear Calderón-Zygmund operator and BMO functions on products of weighted Herz-Morrey spaces with variable exponents
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