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arXiv · 2608.24831

Polynomial Ergodic Averages Along Short Intervals

Anastasios Fragkos·Hamed Mousavi·Amelia Stokolosa
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Abstract

We study pointwise convergence of polynomial ergodic averages over short intervals whose left endpoints tend to infinity. For a polynomial orbit of degree $d\geq2$ and doubly lacunary starting times, we prove $L^p$ variational estimates, and hence almost-everywhere convergence, for $1 (d-1)/d$. This gives the first pointwise ergodic theorem for polynomial orbits along short intervals. We also show that the endpoint $L^1$ fails along every infinite subsequence. In a different direction, we prove that substantially denser sequences of starting times exhibit the strong sweeping-out property.

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BibTeXRIS

Anastasios Fragkos, Hamed Mousavi, Amelia Stokolosa. 2026-08-25. Polynomial Ergodic Averages Along Short Intervals. https://arxiv.org/abs/2608.24831

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