Expansion by polynomials with respect to Freud-type weights

The weights W α ( x ) = exp ( − 1 2 | x | α ) , α > 1 , form an important subclass of Freud weights. For the expansion by orthogonal polynomials with respect to W α ( x ) , we prove analogues of the Hausdorff–Young and the Hardy–Littlewood inequalities. The special cases of expansion by Hermite functions ( α = 2 ) , which are new as well, are given explicitly.