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DYADIC TRIANGULAR HILBERT TRANSFORM OF TWO GENERAL FUNCTIONS AND ONE NOT TOO GENERAL FUNCTION

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  13 November 2015

VJEKOSLAV KOVAČ ,
CHRISTOPH THIELE  and
PAVEL ZORIN-KRANICH
VJEKOSLAV KOVAČ
Affiliation:
Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia; vjekovac@math.hr
CHRISTOPH THIELE
Affiliation:
Department of Mathematics, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany; thiele@math.uni-bonn.de, pzorin@math.uni-bonn.de
PAVEL ZORIN-KRANICH
Affiliation:
Department of Mathematics, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany; thiele@math.uni-bonn.de, pzorin@math.uni-bonn.de

Abstract

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The so-called triangular Hilbert transform is an elegant trilinear singular integral form which specializes to many well-studied objects of harmonic analysis. We investigate $L^{p}$ bounds for a dyadic model of this form in the particular case when one of the functions on which it acts is essentially one dimensional. This special case still implies dyadic analogues of boundedness of the Carleson maximal operator and of the uniform estimates for the one-dimensional bilinear Hilbert transform.

MSC classification

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 3 , 2015 , e25
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2015

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