SHARP INEQUALITIES FOR THE SQUARE FUNCTION OF
A NONNEGATIVE MARTINGALE
Abstract: We determine the optimal constants and such that the following holds: if is
a nonnegative martingale and and denote its square and maximal functions,
respectively, then
and
2000 AMS Mathematics Subject Classification: Primary: 60G42; Secondary:
60G46.
Keywords and phrases: Martingale, square function, maximal function.