Hardy's Inequality for Laguerre Expansions of Hermite Type

摘要

Hardy's inequality for Laguerre expansions of Hermite type with the index alpha is an element of({-1/2}[1/2,infinity))d is proved in the multi-dimensional setting with the exponent 3d/4. We also obtain the sharp analogue of Hardy's inequality with L1 norm replacing H1 norm at the expense of increasing the exponent by an arbitrarily small value.