The Bi-Carleson operator

Details The Bi-Carleson operator The Bi-Carleson operator

2004-09-21

arxiv.org/abs/math/0409406v2

Mathematics

Classical Analysis and ODEs

44 pages, 3 figures, to appear, GAFA. This is the final version, incorporating referee suggestions

Scientific paper

We prove $L^p$ estimates for the Bi-Carleson operator, which is a natural hybrid of the Carleson maximal operator and the bilinear Hilbert transform. The methods used are essentially based on the treatment of the Walsh analogue of the operator in the prequel of this paper, but with additional technicalities due to the fact that in the Fourier model one cannot obtain perfect localization in both space and frequency.

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