Bilinear Hilbert transforms along curves, I: the monomial case

Li, Xiaochun

doi:10.2140/apde.2013.6.197

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Bilinear Hilbert transforms along curves I: the monomial case

Xiaochun Li

Vol. 6 (2013), No. 1, 197–220

DOI: 10.2140/apde.2013.6.197

Abstract

We establish an $L^{2} \times L^{2}$ to $L^{1}$ estimate for the bilinear Hilbert transform along a curve defined by a monomial. Our proof is closely related to multilinear oscillatory integrals.

Keywords

bilinear Hilbert transform along curves

Mathematical Subject Classification 2010

Primary: 42B20, 42B25

Secondary: 46B70, 47B38

Milestones

Received: 13 October 2011

Accepted: 18 November 2011

Published: 1 June 2013

Authors

Xiaochun Li
Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801 United States

Vol. 6, No. 1, 2013