The Boundedness of the B-Riesz Potential in the B-Morrey Spaces

We consider the generalized shift operator (B shift operator),generated by the Laplace-Bessel differential operator ΔB=∑ᵢ₌₁ᵏBᵢ+ ∑ⱼ₌ₖ₊₁ⁿ∂ ²/∂ xⱼ², B=(B₁,…,Bₖ ),Bᵢ=∂ ²/∂ xᵢ²+ γᵢ/xᵢ∂ ∂ xᵢ, γᵢ>0,i=1,…,k$, $|γ|=γ_1++γ_k$. The$B$-maximal functions and the $B$-Riesz potentials, generated bythe Laplace-Bessel differential operator $ΔB$ areinvestigated. We study the $B$-Riesz potentials in the $B$-Morreyspaces. The inequality of Sobolev-Morrey type is established for the $B$-Riesz potentials. 2000 Mathematics Subject Classification. 42B20, 42B25, 42B35