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Bilinear Hilbert Transform on Measure Spaces

Authors:	O Blasco M Carro T A Gillespie

Institution:	(1) Departamento de Análisis Matemático, Universitad de Valencia, Burjassot, 46100-Valencia, Spain;(2) Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E–08071 Barcelona, Spain;(3) Department of Mathematics and Statistics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland

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

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