On Hardy's inequality for Hermite expansions

Abstract

Sharp multi-dimensional Hardy's inequality for the Laguerre functions of Hermite type is proved for the type parameter $\al\in[-1/2,\infty)^d$. As a consequence we obtain the corresponding result for the generalized Hermite expansions. In particular, it validate that the known version of Hardy's inequality for the Hermite functions is sharp.

arXiv comment12 pages

References in corpus (1)

• Hardy's Inequality for Laguerre Expansions of Hermite Type