Uniform ${L}^{p}$ Resolvent Estimates on the Torus
Mathematics Research Reports, Volume 1 (2020), pp. 31-45.

A new range of uniform ${L}^{p}$ resolvent estimates is obtained in the setting of the flat torus, improving previous results of Bourgain, Shao, Sogge and Yao. The arguments rely on the ${\ell }^{2}$-decoupling theorem and multidimensional Weyl sum estimates.

Accepted:
Published online:
DOI: 10.5802/mrr.1
Classification: 35J05,  35P20,  11P21
Jonathan Hickman 1

1 School of Mathematics, The University of Edinburgh, Edinburgh EH9 3JZ, UK
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Jonathan Hickman. Uniform $L^p$ Resolvent Estimates on the Torus. Mathematics Research Reports, Volume 1 (2020), pp. 31-45. doi : 10.5802/mrr.1. https://mrr.centre-mersenne.org/articles/10.5802/mrr.1/

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