Uniform $L^p$ Resolvent Estimates on the Torus

Jonathan Hickman

Uniform $L^p$ Resolvent Estimates on the Torus

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	31-45
Number of pages	30
Journal	Mathematics Research Reports
Volume	1
Publication status	Published - 2020

Keywords / Materials (for Non-textual outputs)

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

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1907.08131v1Submitted manuscript, 267 KB

https://arxiv.org/abs/1907.08131

Cite this

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title = "Uniform \$L\textasciicircum{}p\$ Resolvent Estimates on the Torus",

abstract = " A new range of uniform \$L\textasciicircum{}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 \$\textbackslash{}ell\textasciicircum{}2\$-decoupling theorem and multidimensional Weyl sum estimates. ",

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N2 - 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.

AB - 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.

KW - math.AP

KW - math.CA

KW - 35J05, 35P20, 11P21

M3 - Article

VL - 1

SP - 31

EP - 45

JO - Mathematics Research Reports

JF - Mathematics Research Reports

ER -

Uniform $L^p$ Resolvent Estimates on the Torus

Abstract

Keywords / Materials (for Non-textual outputs)

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