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

    Asmar, Nakhlé H.; Montgomery-Smith, Stephen, 1963- (2011-01)
    In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of Hp spaces for 0 < p < ∞. In this paper, we show that their method extends to higher dimensions ...
  • On singular integral and martingale transforms 

    Montgomery-Smith, Stephen, 1963-; Geiss, Stefan; Saksman, Eero (2011-01)
    Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the ...