Weighted Mean Operators on lp

Borwein, David

Canadian mathematical bulletin, Tome 43 (2000) no. 4, pp. 406-412

Résumé

Abstract. The weighted mean matrix ${{M}_{a}}$ is the triangular matrix $\left\{ {{a}_{k}}/{{A}_{n}} \right\}$ , where ${{a}_{n}}\,>\,0$ and ${{A}_{n}}\,:=\,{{a}_{1}}\,+\,{{a}_{2}}\,+\cdots +\,{{a}_{n}}$ . It is proved that, subject to ${{n}^{c}}{{a}_{n}}$ being eventually monotonic for each constant $c$ and to the existence of $\alpha \,:=\,\lim \,\frac{{{A}_{n}}}{n{{a}_{n}}},\,{{M}_{a}}\,\in \,B\left( {{l}_{p}} \right)$ for $1\,<\,p\,<\infty $ if and only if $\alpha \,<\,p$ .

Détail

DOI : 10.4153/CMB-2000-048-3

Mots-clés : 47B37, 47A30, 40G05, weighted means, operators on l p, norm estimates