Tauberian theorems for the (J,p)(J,p) summability method

In this paper, we prove Tauberian theorems of slowly oscillating type for the (J,p)(J,p) summability method by using a result due to Mikhalin [G.A. Mikhalin, Theorem of Tauberian type for (J, pn) summation methods, Ukrain. Mat. Zh. 29 (1977), 763–770. English translation: Ukrain. Math. J. 29 (1977) 564–569].