B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials on B-Morrey spaces

Abstract

In this article, we consider the Laplace-Bessel differential operatorΔBk,n=∑i=1k∂2∂xi2+γixi∂∂xi+∑i=k+1n∂2∂xi2,γ1>0,…,γk>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.

Keywords

• commutator
• generalized shift operator
• b-riesz potential
• b-maximal function
• b-morrey space
• bounded mean oscillation (bmo) space
• 42b20
• 42b25
• 42b35