Carleson's theorem with quadratic phase functions
Michael T. Lacey (2002)
Studia Mathematica
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It is shown that the operator below maps into itself for 1 < p < ∞. . 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].