Weak Type Inequality for the Square Function of a Nonnegative Submartingale

Adam Osękowski
2009 Bulletin of the Polish Academy of Sciences Mathematics  
Let f be a nonnegative submartingale and S(f ) denote its square function. We show that for any λ > 0, and the constant π/2 is the best possible. The inequality is strict provided f 1 = 0.
doi:10.4064/ba57-1-9 fatcat:2mpd7ozn2fbrxdpawifx3ohwiy