A stationary set method for estimating oscillatory integrals

Saugata Basu; Shaoming Guo; Ruixiang Zhang; Pavel Zorin-Kranich

doi:10.4171/jems/1506

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A stationary set method for estimating oscillatory integrals

Saugata Basu
Purdue University, West Lafayette, USA
Shaoming Guo
Nankai University, Tianjin, P. R. China; University of Wisconsin-Madison, Madison, USA
Ruixiang Zhang
University of California at Berkeley, Berkeley, USA
Pavel Zorin-Kranich
University of Bonn, Bonn, Germany

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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 $k \geq 2$ . As a consequence, we obtain sharp $L^{\infty} \to L^{p}$ Fourier extension estimates for a family of monomial surfaces.

Cite this article

Saugata Basu, Shaoming Guo, Ruixiang Zhang, Pavel Zorin-Kranich, A stationary set method for estimating oscillatory integrals. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1506