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 the type index $\alpha \in [-1/2, \infty)^{d}$. 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.
Funding Statement
This research supported by the National Science Centre of Poland, NCN grant no. 2018/29/N/ST1/02424.
Citation
Paweł PLEWA. "Sharp Hardy's type inequality for Laguerre expansions." J. Math. Soc. Japan 74 (2) 333 - 352, April, 2022. https://doi.org/10.2969/jmsj/84448444
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