Some Tauberian conditions under which convergence follows from (C, 1, 1, 1) summability
Makaleler > Tam Makale · 2019
Yazarlar: ÜMİT TOTUR, İbrahim ÇANAK
The Journal of Analysis, Diğer Kurumların Hakemli Dergileri, Uluslararası, Scopus, 2019, cilt 28, ss 683-694
DOI: 10.1007/s41478-019-00179-z
Özet
Given a real-valued integrable function f(x, y, z) which is integrable over [0,infinity )x[0,infinity )x[0,infinity), let s(x, y, z) denote its integral over [0,x]x[0,y]x[0,z] and let sigma (x,y,z) denote its (C, 1, 1, 1) mean, the average of s(x, y, z) over [0,x]x[0,y]x[0,z], where x,y,z>0. We give one-sided Tauberian conditions of Landau and Hardy type under which convergence of s(x, y, z) follows from (C, 1, 1, 1) summability of s(x, y, z). We obtain convergence of s(x, y, z) from its (C, 1, 1, 1) summability provided that s(x, y, z) is slowly oscillating in certain senses. Furthermore, we extend a Tauberian theorem given by Moricz (Stud Math 138(1):41-52, 2000) for improper double integrals to improper triple integrals.