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arXiv · 2306.00278

Vector-valued maximal inequalities and multi-parameter oscillation inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes

Nathan Mehlhop
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Abstract

We prove the uniform $\ell^2$-valued maximal inequalities for polynomial ergodic averages and truncated singular operators of Cotlar type modeled over multi-dimensional subsets of primes. In the averages case, we combine this with earlier one-parameter oscillation estimates arXiv:2212.09874 to prove corresponding multi-parameter oscillation estimates. This provides a fuller quantitative description of the pointwise convergence of the mentioned averages and is a generalization of the polynomial Dunford-Zygmund ergodic theorem attributed to Bourgain arXiv:2209.01309. .

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Nathan Mehlhop. 2023-06-01. Vector-valued maximal inequalities and multi-parameter oscillation inequalities for the polynomial ergodic averages along multi-dimensional subsets of primes. https://arxiv.org/abs/2306.00278

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