The Boundedness of the $B$-Riesz Potential in the $B$-Morrey Spaces - Hasanov, avanshir J.; Narimanov, Anar Kh. (Sarajevo Journal of Mathematics, 2024)
We consider the generalized shift operator ($B$ shift operator), generated by the Laplace-Bessel differential operator $Δ _{B}=\sum_{i=1}^{k}B_{i}+ \sum_{j=k+1}^{n}\frac {\partial ^2 }{\partial x_j^2},$ $B=\left(B_1,…,B_k \right)$, $B_i=\frac{\partial ^2}{\partial x_i^2}+ \frac{γ_i }{x_i}\frac\partial {\partial x_i},$ $γ_i>0,$ $i=1,…,k$, $|γ|=γ_1+…+γ_k$. The $B$-maximal functions and the $B$-Riesz potentials, generated by the Laplace-Bessel differential operator $Δ_{B}$ are investigated. We study the $B$-Riesz potentials in the $B$-Morrey spaces. The inequality of Sobolev-Morrey type is established for the $B$-Riesz potentials. 2000 Mathematics Subject Classification. 42B20, 42B25, 42B35