Maximal averages along a planar vector field depending on one variable

Michael Bateman

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arXiv · 1104.2859

Maximal averages along a planar vector field depending on one variable

Michael Bateman

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Abstract

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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Michael Bateman. 2011-04-14. Maximal averages along a planar vector field depending on one variable. https://arxiv.org/abs/1104.2859

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