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

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

1999-12-26

arxiv.org/abs/math/9912202v1

Mathematics Research Letters 4 (1997), 221-237

Mathematics

Classical Analysis and ODEs

Scientific paper

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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