Meda inequality for rearrangements of the B-convolutions and some applications

Abstract

In this paper we prove the Meda inequality for rearrangements of the convolution operator (B-convolution) associated with the Laplace-Bessel differential operator. By using the Meda inequality for rearrangements we obtain an O'Neil type inequality for the B-convolution. As applications of these results, we obtain necessary and sufficient conditions on the parameters for the boundedness of the fractional B-maximal operator and B-fractional integral operator with rough kernels, from the spaces Lp,γ to Lq,γ and from the spaces L1,γ to the weak spaces WLq,γ .