Tohoku Mathematical Journal
2018
March
SECOND SERIES VOL. 70, NO. 1

Tohoku Math. J.
70 (2018), 121-138

Title SHARP $L^p$-BOUNDS FOR THE MARTINGALE MAXIMAL FUNCTION

Author Adam Osȩkowski

(Received August 17, 2015, revised January 4, 2016)
Abstract. The paper studies sharp weighted $L^p$ inequalities for the martingale maximal function. Proofs exploit properties of certain special functions of four variables and self-improving properties of $A_p$ weights.

Mathematics Subject Classification. Primary 60G44; Secondary 60G42, 42B25.
Key words and phrases. Martingale, maximal function, weighted inequality, best constant.

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