ACTA issues

## On the boundedness of B-maximal commutators, commutators of B-Riesz potentials and B-singular integral operators in modified B-Morrey spaces

Canay Aykol, Javanshir J. Hasanov

Acta Sci. Math. (Szeged) 86:3-4(2020), 521-547
224/2020

 Abstract. In this paper we consider the generalized shift operator associated to the Laplace--Bessel differential operator $\Delta _{B}$ and investigate B-maximal commutators, commutators of B-Riesz potentials and commutators of B-singular integral operators associated to the generalized shift operator. The boundedness of the $B$-maximal commutator $M_{b,\gamma }$ and the commutator $[b,A_{\gamma }]$ of the $B$-singular integral operator on the modified $B$-Morrey spaces $\widetilde {L}_{p,\lambda ,\gamma }(\Rnk )$ for all $1 < p < \infty$ when $b \in BMO_\gamma ({\Rnk })$ are proved. In addition, we obtain that the commutator $[b,I_{\alpha ,\gamma }]$ of the $B$-Riesz potential $I_{\alpha ,\gamma }$ is bounded from the modified $B$-Morrey space $\widetilde {L}_{p,\lambda ,\gamma }(\Rnk )$ to $\widetilde {L}_{q,\lambda ,\gamma }(\Rnk )$, \$1