2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149471In 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.Also available at http://www.math.missouri.edu/~stephen/preprints/Functional Analysis43A75text