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

N. Asmar·Stephen J. Montgomery-Smith
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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.

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N. Asmar, Stephen J. Montgomery-Smith. 2001-06-22. On a weak type (1,1) inequality for a maximal conjugate function. https://arxiv.org/abs/math/9401207

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