Author

Mariusz Mirek

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Preprint Sep 2026

Dimension-free estimates for discrete maximal functions over cubes in $\mathbb Z^d$

In this short note, we establish dimension-free $\ell^p(\mathbb Z^d)$ bounds, for all $p\in(1,\infty]$, for the discrete Hardy--Littlewood maximal functions associated with cubes in $\mathbb Z^d$, answering a question that had been open for a while. The key idea is to prove dimension-free bounds for the $\ell^p(\mathbb...

Mariusz Mirek, Tomasz Z. Szarek, Bla.zej Wr'obel · 0 citations

Preprint Sep 2026

Pointwise ergodic theorems along sequences of intermediate growth

We establish the first pointwise convergence result for ergodic averages with iterates along explicit and deterministic sequences of intermediate growth, that is, growing faster than any polynomial but slower than any exponential. In particular, we show that the sequence $(\lfloor \exp((\log n)^c)\rfloor)_{n\in\mathbb{...

Leonidas Daskalakis, Mariusz Mirek, M. Wierdl · 0 citations