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 X-c(p) of Lebesgue measurable functions f on R+ = (0, +infinity) such that integral(+infinity)(0) |u(c)f (u)|(p) du/u < infinity, c is an element of R (1 < p <= 2). These results are inspired by a Moricz-type result in classical Fourier analysis, which generalizes a well-known theorem of Titchmarsh.