$B-$ Riezs potential in $B-$ local Morrey-Lorentz spaces

Abstract

In this paper, the Riesz potential (B−Riesz potential) which are generated by the Laplace-Bessel differential operator will be studied. We obtain the necessary and sufficient conditions for the boundedness of the B−Riesz potential $I_{\gamma }^{\alpha }$ in the B-local Morrey-Lorentz spaces $M_{p,q,\lambda,\gamma }^{loc}(\mathbb{R}_{k,+}^{n})$ with the use of the rearrangement inequalities and boundedness of the Hardy operators $H_{\upsilon }^{\beta }$ and $\mathcal{H}_{\upsilon}^{\beta }$ with power weights.