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arXiv · 1810.08138

Sharp Hardy's type inequality for Laguerre expansion

Paweł Plewa
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Abstract

A method of proving Hardy's type inequality for orthogonal expansions is presented in a rather general setting. Then sharp multi-dimensional Hardy's inequality associated with the Laguerre functions of convolution type is proved for type index $\al\in[-1/2,\infty)^d$. The case of the standard Laguerre functions is also investigated. Moreover, the sharp analogues of Hardy's type inequality involving $L^1$ norms in place of $H^1$ norms are obtained in both settings.

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Paweł Plewa. 2018-10-18. Sharp Hardy's type inequality for Laguerre expansion. https://arxiv.org/abs/1810.08138

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