On the Rate of Convergence of (parallel to f parallel to(p)/parallel to f parallel to(infinity))(p) as p - infinity

摘要

Let (X, epsilon, mu) be a measure space and let f : X - R be a measurable function such that parallel to f parallel to(p) infinity for all p = 1 and parallel to f parallel to(infinity) 0. In this paper, we describe the rate of convergence of (parallel to f parallel to(p)/parallel to f parallel to(infinity))(p) as p - infinity.