Carleson's theorem with quadratic phase

Details Carleson's theorem with quadratic phase Carleson's theorem with quadratic phase

2001-05-18

arxiv.org/abs/math/0105159v1

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

Mathematics

Classical Analysis and ODEs

Scientific paper

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

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