Let $A=(a_{n,k})_{n,k\geq 0}$ be a non-negative matrix. Denote by $L_{p}(A)$ , the supremum of those ℓ, satisfying the following inequality \( \left ( \sum _{n = 0}^{\infty }{ \left ( {\sum _{k = 0}^{\infty }{a_{n,k} x_{k} } } \right )^{p} } \right )^{\frac{1}{p}} \ge \ell \left ( { \sum _{k = 0}^{\infty }{ x_{k}^{p} } } \right )^{\frac{1}{p}}\,\,\,\, \,\,\left (x\geq 0, x\in \ell _{p}\right ). \) In this paper, we establish the exact value of $L_{p}\left ((H_{\mu}^{s})^{t}\right )$ , where $H_{\mu}^{s}$ is the generalized Hausdorff matrix and $0< p\le 1$ . We also establish a similar result for $L_{p}(H_{\mu}^{s})$ with $-\infty < p<0$ . Main results of the paper fill up the gaps which the recent works of Chen and Wang have not dealt with.
