English

Maximal averages along a planar vector field depending on one variable

Classical Analysis and ODEs 2011-04-15 v1

Abstract

We prove (essentially) sharp L2L^2 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

R2 v1 2026-06-21T17:54:15.721Z