Sufficient conditions for the Lebesgue integrability of Mellin transforms

This work is devoted to the study of the integrability of Mellin transforms under some sufficient and necessary conditions in the space Xcp of Lebesgue measurable functions f on R+=(0,+∞) such that ∫0+∞|ucf(u)|pduu<∞,c∈R(1<p≤2). These results are inspired by a Móricz-type result in classical Fourier analysis, which generalizes a well-known theorem of Titchmarsh.