Triple Hilbert transforms along polynomial surfaces in $\mathbb{R}^4$

Anthony Carbery; Stephen Wainger; James Wright

doi:10.4171/rmi/573

JournalsrmiVol. 25, No. 2pp. 471–519

Triple Hilbert transforms along polynomial surfaces in $R^{4}$

Anthony Carbery
University of Edinburgh, UK
Stephen Wainger
University of Wisconsin at Madison, USA
James Wright
University of Edinburgh, UK

$Triple Hilbert transforms along polynomial surfaces in $\mathbb{R}^4$ cover$

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Abstract

We investigate the $L^{2}$ boundedness of the triple Hilbert transform along the surface given by the graph of a real polynomial $P$ of three variables. We are interested in understanding the relationship between the geometric properties of the Newton polyhedron of $P$ and the analytic property of $L^{2}$ boundedness.

Cite this article

Anthony Carbery, Stephen Wainger, James Wright, Triple Hilbert transforms along polynomial surfaces in $R^{4}$ . Rev. Mat. Iberoam. 25 (2009), no. 2, pp. 471–519

DOI 10.4171/RMI/573