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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].
$Cf(x) := sup_{a,b} |p.v. ∫ f(x-y)e^{i(ay²+by)} dy/y|$.
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].
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Tom
Numer
Strony
249-267
Opis fizyczny
Daty
wydano
2002
Twórcy
autor
- School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-3-3