论文标题
夏普·哈迪（Sharp Hardy）在$ h^p $空间中对正交扩展的不平等
Sharp Hardy's inequality for orthogonal expansions in $H^p$ spaces
论文作者
论文摘要
在正交扩展的背景下，Hardy对$ h^p $空间的不平等，$ p \ in（0,1] $，以$ \ m m ibsbb {r}^d $的子集的一般为基础。而且，在相关的热内核中，通过构造明确的反例，该研究的锐度是合理的，该示例已调整为所有考虑的设置。
Hardy's inequality on $H^p$ spaces, $p\in(0,1]$, in the context of orthogonal expansions is investigated for general basis on a subset of $\mathbb{R}^d$ with Lebesgue measure. The obtained result is applied to various Hermite, Laguerre, and Jacobi expansions. For that purpose some delicate estimates of the higher order derivatives for the underlying functions and of the associated heat kernels are proved. Moreover, sharpness of studied Hardy's inequalities is justified by a construction of an explicit counterexample, which is adjusted to all considered settings.
