JOURNAL OF MATHEMATICAL STUDY, vol.53, no.1, pp.90-124, 2020 (ESCI)
In this paper we prove an O'Neil inequality for the convolution operator (G-convolution) associated with the Gegenbauer differential operator G(lambda). By using an O'Neil inequality for rearrangements we obtain a pointwise rearrangement estimate of the G-convolution. As an application, we obtain necessary and sufficient conditions on the parameters for the boundedness of the G-fractional maximal and G-fractional integral operators from the spaces L-p,L-lambda to L-q,L-lambda and from the spaces L-1,L-lambda to the weak spaces WLp,lambda.