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Vector-Valued Maximal Inequalities and Multiparameter Oscillation Inequalities for the Polynomial Ergodic Averages Along Multi-dimensional Subsets of Primes

Year: 2024
Type: article
Abstract: We prove uniform $$\ell ^2$$ ℓ 2 -valued maximal inequalities for polynomial ergodic averages and truncated singular operators of Cotlar type modeled over multidimensional subsets of primes. In the averages case, we combine this with earlier one-parameter oscillation estimates (Mehlhop and Słomian in Math Ann, 2023, https://doi.org/10.1007/s00208-023-02597-8 ) to prove corresponding multiparameter 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 (Mirek et al. in Rev Mat Iberoam 38:2249–2284, 2022).
DOI: 10.1007/s00041-024-10119-6
Language: English
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W4403703889
FWCI: 0.764
Cites: 36
Cited by: 1
Related to: 10