Carleson's theorem with quadratic phase

2001/05/18 by Michael Lacey
Mathematics · #math.CA #msc:42

paper · pdf

published as Studia Math. 153 (2002), no. 3, 249--267

arxiv created 2001/05/18 · arxiv updated 2009/11/30

Abstract

Carleson's theorem on the pointwise convergence of Fourier series provides bounds for a maximal operator, with the maximum taken over all choices of linear functions of a phase argument. We extend this to all quadratic choices of phase functions. Specifically, we show that the maximal operator below maps L^p into itself for 1<p<∞. sup_a sup_b |∫ e^i(ay2+by)f(x-y)dy/y|

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