JournalsrmiVol. 18, No. 1pp. 115–134

A uniform estimate for quartile operators

  • Christoph Thiele

    Universität Bonn, Germany
A uniform estimate for quartile operators cover

Abstract

There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove LpL^p estimates for these operators uniformly in the parameter. In the current article we present some of these techniques in a simplified model: we prove the estimate L2×L2L1,L^2\times L^2\to L^{1,\infty} uniformly for a discrete family of model operators for the bilinear Hilbert transform.

Cite this article

Christoph Thiele, A uniform estimate for quartile operators. Rev. Mat. Iberoam. 18 (2002), no. 1, pp. 115–134

DOI 10.4171/RMI/313