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Zeitschrift für Analysis und ihre Anwendungen


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Volume 26, Issue 1, 2007, pp. 103–109
DOI: 10.4171/ZAA/1313

Published online: 2007-03-31

Maximal Characterization of Locally Summable Functions

F. Andreano[1] and R. Grande[2]

(1) Università di Roma La Sapienza, Italy
(2) Università di Roma La Sapienza, Italy

We prove a characterization of locally summable functions with bounded Stepanoff norm through the maximal function $$ M_\phi f(x)=\sup_{t>0} |(f*\phi_t)(x) |, $$ where $\phi$ is a suitable function in the class of Schwartz.

Keywords: Stepanoff bounded functions, maximal function

Andreano F., Grande R.: Maximal Characterization of Locally Summable Functions. Z. Anal. Anwend. 26 (2007), 103-109. doi: 10.4171/ZAA/1313