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Negative results for Nikodym maximal functions and related oscillatory integrals in curved space

William Minicozzi II·Christopher D. Sogge
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Abstract

We expand on counterxamples of Bourgain showing how Nikodym maximal estimates and oscillatory integral estimates can break down in the non-Euclidean case. Our examples show the role that the non-existence of totally geodesic submanifolds can play in these problems.

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William Minicozzi II, Christopher D. Sogge. 1999-12-26. Negative results for Nikodym maximal functions and related oscillatory integrals in curved space. https://arxiv.org/abs/math/9912202

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