JournalsrmiVol. 25, No. 2pp. 471–519

Triple Hilbert transforms along polynomial surfaces in R4\mathbb{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 L2L^2 boundedness of the triple Hilbert transform along the surface given by the graph of a real polynomial PP of three variables. We are interested in understanding the relationship between the geometric properties of the Newton polyhedron of PP and the analytic property of L2L^2 boundedness.

Cite this article

Anthony Carbery, Stephen Wainger, James Wright, Triple Hilbert transforms along polynomial surfaces in R4\mathbb{R}^4. Rev. Mat. Iberoam. 25 (2009), no. 2, pp. 471–519

DOI 10.4171/RMI/573