Carleson's theorem with quadratic phase functions

• Autorzy: Michael T. Lacey
• Języki publikacji: EN

Abstrakty

EN

It is shown that the operator below maps $L^{p}$ into itself for 1 < p < ∞.
$Cf(x) := sup_{a,b} |p.v. ∫ f(x-y)e^{i(ay²+by)} dy/y|$.
The supremum over b alone gives the famous theorem of L. Carleson [2] on the pointwise convergence of Fourier series. The supremum over a alone is an observation of E. M. Stein [12]. The method of proof builds upon Stein's observation and an approach to Carleson's theorem jointly developed by the author and C. M. Thiele [7].

Kategorie tematyczne

• 42A20: Convergence and absolute convergence of Fourier and trigonometric series
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 153
• Numer: 3
• Strony: 249-267

Daty

wydano

2002

Twórcy

autor

Michael T. Lacey

• School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

Identyfikatory

DOI

10.4064/sm153-3-3