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On the boundedness of a B-Riesz potential in the generalized weighted B-Morrey spaces
(Walter de Gruyter GmbH, 2016) Ayazoglu R.; Hasanov J.J.
We consider the generalized shift operator associated with the Laplace-Bessel differential operator ? B = i=1 n 2 x i 2 +i=1 k ? i x ix i .$ \Delta -{B}=\sum -{i=1}^{n}\frac{\partial ^2 }{\partial x-i^2} +\sum -{i=1}^{k} \frac{\gamma -i }{x-i}\frac{\partial }{\partial x-i}. $ The maximal operator M ? ${M-{\gamma }}$ (B-maximal operator) and the Riesz potential I ?,? ${I-{\alpha ,\gamma }}$ (B-Riesz potential), associated with the generalized shift operator are investigated. We prove that the B-maximal operator M ? ${M-{\gamma }}$ and the B-singular integral operator are bounded from the generalized weighted B-Morrey space p,? 1 ,?,? (k,+ n )${{\cal M}-{p,\omega -1,\varphi ,\gamma }(\mathbb {R}-{k,+}^{n})}$ to p,? 2 ,?,? (k,+ n )${{\cal M}-{p,\omega -2,\varphi ,\gamma }(\mathbb {R}-{k,+}^{n})}$ for all 1