Weak type $(1, 1)$ estimates for maximal functions along $1$-regular sequences of integers
Tom 261 / 2021
Studia Mathematica 261 (2021), 103-108
MSC: Primary 37A44, 37A46.
DOI: 10.4064/sm200702-21-12
Opublikowany online: 24 May 2021
Streszczenie
We show the pointwise convergence of the averages \[ \mathcal A _N f(x) = \frac {1}{\# {\bf B} _N} \sum _{n \in {\bf B} _N} f(x + n) \] for $f \in \ell ^1(\mathbb Z )$ where ${\bf B} _N = {\bf B} \cap [1, N]$, and ${\bf B} $ is a $1$-regular sequence of integers, for example ${\bf B} = \{\lfloor n \log n \rfloor : n \in \mathbb N \}$.
