Search Results for author: Bartosz Trojan

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Weak type $(1, 1)$ estimates for maximal functions along $1$-regular sequences of integers

no code implementations18 Dec 2020 Bartosz Trojan

We show the pointwise convergence of the averages \[ \mathcal{A}_N f(x) = \frac{1}{\# \mathbf{B}_N} \sum_{n \in \mathbf{B}_N} f(x + n) \] for $f \in \ell^1(\mathbb{Z})$ where $\mathbf{B}_N = \mathbf{B} \cap [1, N]$, and $\mathbf{B}$ is a $1$-regular sequence of integers, for example $\mathbf{B} = \{\lfloor n \log n \rfloor : n \in \mathbb{N}\}$.

Number Theory Functional Analysis 37A44, 37A46

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