SHARP INEQUALITIES FOR THE VARIATION OF THE DISCRETE MAXIMAL FUNCTION
SHARP INEQUALITIES FOR THE VARIATION OF THE DISCRETE MAXIMAL FUNCTION
In this paper we establish new optimal bounds for the derivative of some discrete maximal functions, in both the centred and uncentred versions. In particular, we solve a question originally posed by Bober et al. [‘On a discrete version of Tanaka’s theorem for maximal functions’, Proc. Amer. Math. Soc. 140 …