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.
Citation
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
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