Mathematical Research Letters

Volume 14 (2007)

Number 2

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

Pages: 227 – 237

DOI: http://dx.doi.org/10.4310/MRL.2007.v14.n2.a6

Authors

Roman Urban

Jacek Zienkiewicz

Abstract

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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