Maximal averages along a planar vector field depending on one variable

Details Maximal averages along a planar vector field depending on one variable Maximal averages along a planar vector field depending on one variable

2011-04-14

arxiv.org/abs/1104.2859v1

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

We prove (essentially) sharp $L^2$ 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.

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