On the relation between Lebesgue summability and some other summation methods

Abstract

It is shown that if $$\sum _{n=1}^{N}n\left|c_n\right|=O(N),$$ then Lebesgue summability, $(\mathrm{C},\beta )$ summability ($\beta >0$), Abel summability, Riemann summability, and $(\gamma ,\kappa )$ summability ($\kappa \ge 1$) of the series ${\sum }_{n=0}^{\infty }{c}_n$ are all equivalent to one another.

11 pages. New references added

References in corpus (1)

• Distributional versions of Littlewood's Tauberian theorem