A stationary set method for estimating oscillatory integrals
Saugata BasuPurdue University, West Lafayette, USAShaoming GuoNankai University, Tianjin, P. R. ChinaRuixiang ZhangUniversity of California at Berkeley, USAPavel Zorin‐KranichUniversity of Bonn, Germany
2024en
ABI
Abstract
We propose a new method of estimating oscillatory integrals, which we call a “stationary set” method. We use it to obtain the sharp convergence exponents of Tarry’s problems in dimension two for every degree k\ge 2 . As a consequence, we obtain sharp L^{\infty} \to L^{p} Fourier extension estimates for a family of monomial surfaces.
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