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2015 Refined and microlocal Kakeya–Nikodym bounds for eigenfunctions in two dimensions
Matthew Blair, Christopher Sogge
Anal. PDE 8(3): 747-764 (2015). DOI: 10.2140/apde.2015.8.747

Abstract

We obtain some improved essentially sharp Kakeya–Nikodym estimates for eigenfunctions in two dimensions. We obtain these by proving stronger related microlocal estimates involving a natural decomposition of phase space that is adapted to the geodesic flow.

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Matthew Blair. Christopher Sogge. "Refined and microlocal Kakeya–Nikodym bounds for eigenfunctions in two dimensions." Anal. PDE 8 (3) 747 - 764, 2015. https://doi.org/10.2140/apde.2015.8.747

Information

Received: 12 September 2014; Revised: 31 December 2014; Accepted: 9 February 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1321.58029
MathSciNet: MR3353830
Digital Object Identifier: 10.2140/apde.2015.8.747

Subjects:
Primary: 58J51
Secondary: 35L20, 42B37

Rights: Copyright © 2015 Mathematical Sciences Publishers

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