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

William Minicozzi II, Christopher D. Sogge

Published 1999-12-26Version 1

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.

Journal: Mathematics Research Letters 4 (1997), 221-237
Categories: math.CA
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