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L2 to Lp bounds for spectral projectors on the Euclidean two-dimensional torus
Published online by Cambridge University Press: 15 March 2024
Abstract
We consider spectral projectors associated to the Euclidean Laplacian on the two-dimensional torus, in the case where the spectral window is narrow. Bounds for their L2 to Lp operator norm are derived, extending the classical result of Sogge; a new question on the convolution kernel of the projector is introduced. The methods employed include $\ell^2$ decoupling, small cap decoupling and estimates of exponential sums.
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society