On boundedness of the generalized B-potential integral operators in the Lorentz spaces

Abstract

In this paper, we study the convolution operator (B–convolution), and the generalized B-potential integral and fractional integral (B-fractional integral) with rough kernel, associated with the Laplace–Bessel differential operator We get O'Neil type inequality for the B–convolution. By using O'Neil type inequality we obtain a pointwise rearrangement estimate of the generalized B-potential integral. We prove the boundedness of the generalized B-potential integral operator in the Lorentz spaces, and the proof is based on the pointwise estimate of the rearrangement of this operator.