Weak-type estimates for martingale maximal functions
Weak-type estimates for martingale maximal functions
The paper contains the study of sharp extensions of weak-type estimates for a martingale maximal function. Given 1<p<∞ and a pair (x,y) of nonnegative numbers satisfying xp≤y, we identify the optimal upper bounds for ‖|supnfn|‖p,∞, for nonnegative martingales f=(fn)n≥0 satisfying ‖f‖1=x and ‖f‖pp=y.