Abstract
In this article we obtain the boundedness of the periodic, discrete and ergodic bilinear Hilbert transform, from \(L^{p_1}\times L^{p_2}$ into $L^{p_3}\), where \(1/p_1+ 1/p_2=1/p_3$, $p_1, p_2 > 1$, and $p_3\ge 1\). The main techniques are a bilinear version of the transference method of Coifman and Weiss and certain discretization of bilinear operators. In the periodic case, we also obtain the boundedness for \(2/3<p_3<1\)
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Blasco, O., Carro, M. & Gillespie, T. Bilinear Hilbert Transform on Measure Spaces. J Fourier Anal Appl 11, 459–470 (2005). https://doi.org/10.1007/s00041-005-4074-1
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DOI: https://doi.org/10.1007/s00041-005-4074-1