On two integrability methods

Let p be a non-negative, non-decreasing function on [0, infinity) and let k >= 1. In this paper, we introduce the concept of the Riesz integrability (shortly, vertical bar(N) over bar , p vertical bar(k) integrability) of improper integrals. We prove an equivalence theorem of vertical bar(N) over bar , p vertical bar(k) and vertical bar(N) over bar , q vertical bar(k) integrability of improper integrals.