(untitled) (Journal of Mathematical Study, 2020)
In this paper we prove an O'Neil inequality for the convolution operator (G-convolution) associated with the Gegenbauer differential operator G_λ. 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,λ to L_q,λ and from the spaces L_1,λ to the weak spaces WL_p,λ.