On the bi-carleson operator I. The Walsh case
Camil Muscalu, Terence Tao, Christoph Thiele
Abstract
We prove Lp estimates for the Walsh model of the maximal bi-Carleson operator (which is a hybrid of the bilinear Hilbert transform and the Carleson maximal operator which appears naturally in the eigenfunction problem for one-dimensional Schrodinger operators). The corresponding estimates for the Fourier model will be obtained in the sequel of this paper.
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