Maximal Characterization of Locally Summable Functions

Abstract

We prove a characterization of locally summable functions with bounded Stepanoff norm through the maximal function

M_{ϕ} f (x) = t > 0 sup ∣ (f * ϕ_{t}) (x) ∣,

where $ϕ$ is a suitable function in the class of Schwartz.

F. Andreano, R. Grande, Maximal Characterization of Locally Summable Functions. Z. Anal. Anwend. 26 (2007), no. 1, pp. 103–109