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=_i=1^kB_i+ _j=k+1^n^2 x_j^2, B=(B_1,…,B_k ), B_i=^2x_i^2+ γ_i x_ix_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