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# Summability Factors for Cesàro Methods

David F. Dawson
Proceedings of the American Mathematical Society
Vol. 73, No. 3 (Mar., 1979), pp. 371-374
DOI: 10.2307/2042366
Stable URL: http://www.jstor.org/stable/2042366
Page Count: 4
It is shown that if each of $r$ and $s$ is a nonnegative integer and $\{f_p\}$ is a complex sequence such that $\sum f_pa_p$ is Cesàro summable of order $s$ whenever $\sum a_p$ is Cesàro summable of order $r$, then $\sum f_pa_p$ is Cesàro summable of order $r$ whenever $\sum a_p$ is Cesàro summable of order $r$.