On the boundedness of hyperbolic Riesz B-potential

Abstract

This paper deals with the hyperbolic Riesz B-potential, which is the negative real power of an operator Bγ1 − ∑i = 2nBγi, where \( \begin{array}{cc}\hfill {B}_{\upgamma i}={\partial}^2/\partial {x}_i^2+\left({\upgamma}_i/{x}_i\right)\partial /\partial {x}_i,\hfill & \hfill i=1,\dots, n,\hfill \end{array} \) is a singular Bessel differential operator. We prove the boundedness of the hyperbolic Riesz B-potential in proper spaces.