Beyond local maximal operators
Classical Analysis and ODEs
2015-05-18 v1 Functional Analysis
Abstract
We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions.
Cite
@article{arxiv.1505.04042,
title = {Beyond local maximal operators},
author = {Hannes Luiro and Antti V. Vähäkangas},
journal= {arXiv preprint arXiv:1505.04042},
year = {2015}
}