We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series. © 2013 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic.
Publication Source (Journal or Book title)
Czechoslovak Mathematical Journal
Estrada, R., & Vindas, J. (2013). Distributional versions of littlewood's Tauberian theorem. Czechoslovak Mathematical Journal, 63 (2), 403-420. https://doi.org/10.1007/s10587-013-0025-1