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arXiv · 1810.03859

Hardy's Inequality for Laguerre Expansions of Hermite Type

Paweł Plewa
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Abstract

Hardy's inequality for Laguerre expansions of Hermite type with the index $\al\in(\{-1/2\}\cup[1/2,\infty))^d$ is proved in the multi-dimensional setting with the exponent $3d/4$. We also obtain the sharp analogue of Hardy's inequality with $L^1$ norm replacing $H^1$ norm at the expense of increasing the exponent by an arbitrarily small value.

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Paweł Plewa. 2018-10-09. Hardy's Inequality for Laguerre Expansions of Hermite Type. https://doi.org/10.1007/s00041-018-9642-2

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