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

Tom 125 / 1997

Nakhlé H. Asmar, Stephen J. Montgomery-Smith Studia Mathematica 125 (1997), 13-21 DOI: 10.4064/sm-125-1-13-21


In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of $H^p$ spaces for 0 < p < ∞. In the present paper, we show that the methods in [3] extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.


  • Nakhlé H. Asmar
  • Stephen J. Montgomery-Smith

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