Fractional maximal functions in metric measure spaces
Functional Analysis
2013-06-12 v2
Abstract
We study the mapping properties of fractional maximal operators in Sobolev and Campanato spaces in metric measure spaces. We show that, under certain restrictions on the underlying metric measure space, fractional maximal operators improve the Sobolev regularity of functions and map functions in Campanato spaces to H\"older continuous functions. We also give an example of a space where fractional maximal function of a Lipschitz function fails to be continuous.
Cite
@article{arxiv.1301.7191,
title = {Fractional maximal functions in metric measure spaces},
author = {Toni Heikkinen and Juha Lehrbäck and Juho Nuutinen and Heli Tuominen},
journal= {arXiv preprint arXiv:1301.7191},
year = {2013}
}