Weak type (1,1) estimates for a class of discrete rough maximal functions

We prove weak type $(1,1)$ estimate for the maximal function associated with the sequence $[m^\alpha],$ $1<\alpha <1+\frac{1}{1000}$. As a consequence, the sequence $[m^\alpha]$ is universally $L^1$-good.

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Published 1 January 2007