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

DOI10.4064/SM-125-1-13-21zbMATH Open0896.42015arXivmath/9401207OpenAlexW1646524970MaRDI QIDQ4347692

Stephen Montgomery-Smith, Nakhlé H. Asmar

Publication date: 1 October 1998

Published in: Studia Mathematica (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math/9401207

zbMATH Keywords

maximal function Brownian motion conjugate function martingale difference weak type (1,1)harmonic conjugation

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Probabilistic methods for one variable harmonic analysis (42A61) Analysis on ordered groups, (H^p)-theory (43A17)

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