On a weak type (1,1) inequality for a maximal conjugate function
Functional Analysis
2008-02-03 v2
Abstract
In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of H^p spaces for 0 < p < infinity. In this paper, we show that their method extends to higher dimensions and yields a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.
Cite
@article{arxiv.math/9401207,
title = {On a weak type (1,1) inequality for a maximal conjugate function},
author = {N. Asmar and Stephen J. Montgomery-Smith},
journal= {arXiv preprint arXiv:math/9401207},
year = {2008}
}
Comments
Also available at http://www.math.missouri.edu/~stephen/preprints/