A sharp bound for the Stein-Wainger oscillatory integral

Details A sharp bound for the Stein-Wainger oscillatory integral A sharp bound for the Stein-Wainger oscillatory integral

2007-09-10

arxiv.org/abs/0709.1466v2

Proc. AMS, 136 (2008), 963-972

Mathematics

Classical Analysis and ODEs

11 pages; Paper published in Proc. AMS, 136 (2008), 963-972

Scientific paper

Let Pd denote the space of all real polynomials of degree at most d. It is an old result of Stein and Wainger that for every polynomial P in Pd: |p.v.\int_R {e^{iP(t)} dt/t} | < C(d) for some constant C(d) depending only on d. On the other hand, Carbery, Wainger and Wright claim that the true order of magnitude of the above principal value integral is log d. We prove this conjecture.

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