Year: 2026
Type: article
Abstract: We generalize the centered and uncentered Hardy-Littlewood maximal function in terms of shape of integration sets. Continuity of two global and two local generalized maximal functions in $$\textbf{R}^{n}$$ R n is studied. The global ones are continuous. One of the local ones is continuous, provided the integration set is star-shaped with respect to its center. For the second local one, we construct a counterexample.
Source: manuscripta mathematica
Author: Juha Kapulainen
Institution: University of Helsinki
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Helsingin Yliopisto
OpenAlex ID: W7166352658