Lower bounds of Copson type for matrices

矩陣的卡普森形式下界估計

王國仲(Kuo-Zhong Wang)

指導教授 ： 黃明傑 ； 陳璋泡

國立清華大學/理學院/數學系/博士(2008年)

摘要

Let $p,qin mathbf{R}ackslash {0}$ and $A=(a_{n,k})_{n,kgeq0}$
be a non-negative matrix. Denote by $L_{p,q}(A)$ the supremum of
those $L$ satisfying the following inequality:
$$
left(sum_{n=0}^inftyleft(sum_{k=0}^infty a_{n,k}x_k
ight)^q
ight)^{1/q}geq
Lleft(sum_{k=0}^infty {x_k}^p
ight)^{1/p}qquad(Xin ell_p,
Xge 0).$$ The purpose of this thesis is to find the exact value of $L_{p,q}(A)$
for summability matrices, Hausdorff matrices, weighted mean
matrices, N"orlund matrices, and their transposes, where $0

關鍵字

下界 ； Hausdorff 矩陣 ； weighted mean 矩陣 ； Norlund 矩陣 ； Summability 矩陣

參考文獻

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