Generalized translate operator, B-maximal operator, B-Riesz potential operator, Commutators, Generalized weighted B-Morrey space
• Javanshir Hasanov,
• Ismail Ekincioglu,
• Cansu Keskin
Javanshir Hasanov
Institute for Mathematics Mechanics and Informatics

Corresponding Author:hasanov.javanshir@math.ab.az

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Ismail Ekincioglu
Dumlupinar University
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Cansu Keskin
Dumlupinar University
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## Abstract

In this study, we investigate the boundedness of B-Riesz potential and its commutators on generalized weighted B-Morrey spaces. The primary aim of this study is to investigate the boundedness of Riesz potential and its commutators generated by generalized translate operator on generalized weighted B-Morrey spaces. In particular, B-Riesz potantial, its commutators and B-Morrey spaces are related to generalized translate operators that is associated with Laplace Bessel differential operator. Then, two-weighted inequality for these operators and its commutators on generalized weighted B-Morrey spaces is also provided. As a corollary, the boundedness of B-Riesz potential and its commutators on generalized weighted B-Morrey spaces is proved.