Uniform $L^p$ Resolvent Estimates on the Torus

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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.
Original languageEnglish
Pages (from-to)31-45
Number of pages30
JournalMathematics Research Reports
Publication statusPublished - 2020


  • math.AP
  • math.CA
  • 35J05, 35P20, 11P21


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