论文标题
$ \ ell^p $中某些广义希尔伯特运营商的界限
On the boundedness of certain generalized Hilbert operators in $\ell^p$
论文作者
论文摘要
Hilbert Matrix $ \ MATHCAL {H} _ {n，m} =（n+ m+ 1）^{ - 1} $在以前的文献中已经进行了广泛的研究。在本文中，我们研究了由$ [0，1] $的措施产生的普遍的希尔伯特操作员，因此Hilbert Matrix是由Lebesgue Mesures获得的。我们为这些运营商提供了必要和充分的条件，以$ \ ell^p $界定并计算其规范。
The Hilbert matrix $\mathcal{H}_{n,m} = (n+m+ 1)^{-1}$ has been extensively studied in previous literature. In this paper we look at generalized Hilbert operators arising from measures on the interval $[0, 1]$, such that the Hilbert matrix is obtained by the Lebesgue measure. We provide a necessary and sufficient condition for these operators to be bounded in $\ell^p$ and calculate their norm.
