Boundedness of spectral projectors on hyperbolic surfaces
Abstract
In this paper, we prove L2 → Lp estimates, where p>2, for spectral projectors on a wide class of hyperbolic surfaces. More precisely, we consider projections in small spectral windows [λ−η, λ+η] on geometrically finite hyperbolic surfaces of infinite volume. In the convex cocompact case, we obtain optimal bounds with respect to λ and η, up to subpolynomial losses. The proof combines the resolvent bound of Bourgain-Dyatlov and improved estimates for the Schrödinger group (Strichartz and smoothing estimates) on hyperbolic surfaces.
Domains
Mathematics [math]
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