A uniform estimate for quartile operators

Thiele, Christoph

Rev. Mat. Iberoamericana, Tome 18 (2002) no. 1, p. 115-134 / Harvested from Project Euclid

Résumé

There is a one parameter family of bilinear Hilbert transforms. Recently, some progress has been made to prove $L^p$ 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 $L^2\times L^2\to L^{1,\infty}$ uniformly for a discrete family of model operators for the bilinear Hilbert transform.

Détail

Publié le : 2002-03-14
Classification:  Bilinear Hilbert Transform,  Multilinear Singular Integrals,  Uniform Estimates,  42A50