Hardy's inequalities for Hermite and Laguerre expansions revisited

Abstract

We show that Hardy's inequalities for Laguerre expansions hold on the space L¹(0,∞) when the Laguerre parameters α are positive, and we prove that although the inequality holds on the real Hardy space H¹(0,∞) if α = 0, it does not hold on L¹(0,∞). Further, Hardy's inequality for Hermite expansion is established on L¹(0,∞).