Abstract In this article, we consider the Laplace-Bessel differential operator Δ B k , n = ∑ i = 1 k ∂ 2 ∂ x i 2 + γ i x i ∂ ∂ x i + ∑ i = k + 1 n ∂ 2 ∂ 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 ∈ BMO γ b\in {\text{BMO}}_{\gamma } .

中文翻译：

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B-极大交换子、B-奇异积分算子的交换子和B-Morrey空间上的B-Riesz势

摘要 在本文中，我们考虑拉普拉斯-贝塞尔微分算子 Δ B k , n = ∑ i = 1 k ∂ 2 ∂ xi 2 + γ ixi ∂ ∂ xi + ∑ i = k + 1 n ∂ 2 ∂ xi 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。此外，我们定义了 B-极大交换子、B-奇异积分算子的交换子和 B-与拉普拉斯-贝塞尔微分算子相关的 Riesz 势。此外，我们还得到了 B-极大交换子 M b , γ {M}_{b,\gamma } 和交换子 [ b , A γ ] {[}b,