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

• Main Authors: Hasanov Javanshir J., Ayazoglu Rabil, Bayrakci Simten
• Format: Article
• Language: English
• Published: De Gruyter 2020-07-01
• Series: Open Mathematics
• Subjects: commutator; generalized shift operator; b-riesz potential; b-maximal function; b-morrey space; bounded mean oscillation (bmo) space; 42b20; 42b25; 42b35
• Online Access: https://doi.org/10.1515/math-2020-0033

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.