Hardy's inequalities for Hermite and Laguerre expansions revisited

We show that Hardy's inequalities for Laguerre expansions hold on the space L^1(0,\infty) when the Laguerre parameters \alpha are positive, and we prove that although the inequality holds on the real Hardy space H^1(0,\infty) if \alpha= 0, it does not hold on L^1(0,\infty). Further, Hardy's inequality for Hermite expansion is established on L^1(0,\infty).