JournalszaaVol. 26, No. 1pp. 103–109

Maximal Characterization of Locally Summable Functions

  • F. Andreano

    Università di Roma La Sapienza, Italy
  • R. Grande

    Università di Roma La Sapienza, Italy
Maximal Characterization of Locally Summable Functions cover

Abstract

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

Mϕf(x)=supt>0(fϕt)(x),M_\phi f(x)=\sup_{t>0} |(f*\phi_t)(x) |,

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

Cite this article

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

DOI 10.4171/ZAA/1313