Hasanov, Javanshir J.; Ayazoglu, Rabil; Bayrakci, Simten

In this article, we consider the Laplace-Bessel differential operator Δ B k, n = a' i = 1 k a, 2 a, x i 2 + γ i x i a, a, x i + a' i = k + 1 n a, 2 a, x i 2, γ 1 > 0,γ k > 0. {\Delta }{{B}{k,n}}=\mathop{\sum }\limits{i=1}{k}\left(\frac{{\partial }{2}}{\partial {x}{i}{2}}+\frac{{\gamma }{i}}{{x}{i}}\frac{\partial }{\partial {x}{i}}\right)+\mathop{\sum }\limits{i=k+1}{n}\frac{{\partial }{2}}{\partial {x}{i}{2}},{\gamma }{1}\gt 0,\ldots,{\gamma }{k}\gt 0. Furthermore, we define B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials associated with the Laplace-Bessel differential operator. Moreover, we also obtain the boundedness of the B-maximal commutator M b, γ {M}{b,\gamma } and the commutator [ b, A γ[ {[}b,{A}{\gamma }] of the B-singular integral operator and Hardy-Littlewood-Sobolev-type theorem for the commutator [ b, I α, γ[ {[}b,{I}{\alpha,\gamma }] of the B-Riesz potential on B-Morrey spaces L p, λ, γ {L}{p,\lambda,\gamma }, when b â BMO γ b\in {\text{BMO}}{\gamma }.

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