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A sharp bound for the Stein-Wainger oscillatory integral

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 نشر من قبل Ioannis Parissis
 تاريخ النشر 2008
  مجال البحث
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 تأليف Ioannis Parissis




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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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