Revista Matemática Iberoamericana

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Volume 25, Issue 2, 2009, pp. 471–519
DOI: 10.4171/RMI/573

Published online: 2009-08-31

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

Anthony Carbery[1], Stephen Wainger[2] and James Wright[3]

(1) University of Edinburgh, UK
(2) University of Wisconsin at Madison, USA
(3) University of Edinburgh, UK

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.

Keywords: Hilbert transform, Newton polyhedron and oscillatory integrals

Carbery Anthony, Wainger Stephen, Wright James: Triple Hilbert transforms along polynomial surfaces in $\mathbb{R}^4$. Rev. Mat. Iberoamericana 25 (2009), 471-519. doi: 10.4171/RMI/573