On a weak type (1,1) inequality for a maximal conjugate function

Details On a weak type (1,1) inequality for a maximal conjugate function On a weak type (1,1) inequality for a maximal conjugate function

1994-01-18

arxiv.org/abs/math/9401207v2

Studia Math. 125, (1997), 13-21

Mathematics

Functional Analysis

Also available at http://www.math.missouri.edu/~stephen/preprints/

Scientific paper

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.

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