Maximal averages along a planar vector field depending on one variable
Classical Analysis and ODEs
2011-04-15 v1
Abstract
We prove (essentially) sharp estimates for a restricted maximal operator associated to a planar vector field that depends only on the horizontal variable. The proof combines an understanding of such vector fields from earlier work of the author with a result of Nets Katz on directional maximal operators.
Keywords
Cite
@article{arxiv.1104.2859,
title = {Maximal averages along a planar vector field depending on one variable},
author = {Michael Bateman},
journal= {arXiv preprint arXiv:1104.2859},
year = {2011}
}
Comments
20 pages