On high indices theorems

Abstract

which satisfy the condition ni+llni _ q > 1, i = 1, 2, Throughout, let { Xn } be a sequence of positive numbers such that 1 ? 0 and lim f(x) as x-*O exists and is finite. The Dirichlet series (1.1) is called lacunary if the Xn satisfy the condition (1.2) XAn+ 1/n > q > 1, n = 1, 2, The series Jan is called A, XI summable if the series (1.1) converges for x> 0 and f(x) is of bounded variation in (0, co). We write

Locations

• Proceedings of the American Mathematical Society - View - PDF