Abstract
Let $p,q\in \mathbf{R}\backslash \{0\}$ and $A=(a_{n,k})_{n,k\geq0}$be a non-negative matrix. Denote by $L_{p,q}(A)$ the supremum ofthose $L$ satisfying the following inequality:$$ \left(\sum_{n=0}^\infty\left(\sum_{k=0}^\infty a_{n,k}x_k\right)^q\right)^{1/q}\geqL\left(\sum_{k=0}^\infty {x_k}^p\right)^{1/p}\qquad(X\in \ell_p,X\ge 0).$$ The purpose of this thesis is to find the exact value of $L_{p,q}(A)$for summability matrices, Hausdorff matrices, weighted meanmatrices, N"orlund matrices, and their transposes, where $0<p,q\le\infty$.