Characterization of Carleson measures by the Hausdorff-Young property

It is shown that the Laplace transform of an Lp (1 < p ≤ 2) function defined on the positive semiaxis satisfies the Hausdorff-Young type inequality with a positive weight in the right complex half-plane if and only if the weight is a Carleson measure. In addition, Carleson’s weighted Lp inequality for the harmonic extension is given with a numeric constant.