Carleson's theorem with quadratic phase functions

Michael T. Lacey

Studia Mathematica, Tome 151 (2002), p. 249-267 / Harvested from The Polish Digital Mathematics Library

Résumé

It is shown that the operator below maps $L^{p}$ into itself for 1 < p < ∞. $C f (x) : = s u p_{a, b} | p . v . \int f (x - y) e^{i (a y ² + b y)} d y / y |$ . 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].

Publié le : 2002-01-01

Zbl 1019.42006

EUDML-ID : urn:eudml:doc:286481

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Michael T. Lacey. Carleson's theorem with quadratic phase functions. Studia Mathematica, Tome 151 (2002) pp. 249-267. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-3-3/