Adams theorem for the B-Riesz potential in the total B-Morrey spaces

Abstract

We prove Adams theorem for the Riesz potential \(I_{\gamma}^{\alpha}\) (B-Riesz potential) in the total Morrey spaces \(L_{p,(\lambda,\mu),\gamma}\) (total B-Morrey spaces), associated with the Laplace-Bessel differential operator \(\Delta_B\). More precisely, we obtain necessary and sufficient conditions for the operator \(I_{\gamma}^{\alpha}\) to be bounded from the total B-Morrey space \(L_{p,(\lambda,\mu),\gamma}\) to the total B-Morrey space \(L_{q,(\lambda,\mu),\gamma}\) and from the total B-Morrey space \(L_{1,(\lambda,\mu),\gamma}\) to the weak total B-Morrey space \(WL_{q,(\lambda,\mu),\gamma}\).