The Hausdorff-Young inequality and Freud weights (Q6057446)

\textit{Z. Ditzian} proved in [J. Math. Anal. Appl. 398, 582--587 (2013; Zbl 1351.42035)] analogues of the Hausdorff-Young inequality for Freud weights. In particular, he proved that the Freud coefficients belong to a weighted \( \ell^q \) space, where \( q=p,\) the conjugate index to \( p\). Here the authors establish sharpened versions of those results in the sense of replacing \( p^\prime \) by \( q<p^\prime \). They consider expansions in Freud functions and in Freud polynomials, find Lorentz and Orlicz space estimates, and \( n \)-dimensional expansions.