Pointwise convergence of double ergodic averages along certain non-polynomial sequences
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911220521500672 |
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| author | Xiao, Rongzhong |
| author_facet | Xiao, Rongzhong |
| contents | Fix $c\in (1,23/22)$. Let $α$ and $β$ be two distinct non-zero real numbers with $|α|\neq |β|$. It is shown that for any measure preserving system $(X,\mathcal{X},μ,T)$ and any $f,g\in L^{\infty}(μ)$, the limit \begin{equation*} \lim_{N\to\infty}\frac{1}{N}\sum_{n=1}^{N}f(T^{\lfloor αn^c \rfloor}x)g(T^{\lfloor βn^c \rfloor}x) \end{equation*} exists for $μ$-a.e. $x\in X$. Meanwhile, a multidimensional version of the above result is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pointwise convergence of double ergodic averages along certain non-polynomial sequences Xiao, Rongzhong Dynamical Systems Fix $c\in (1,23/22)$. Let $α$ and $β$ be two distinct non-zero real numbers with $|α|\neq |β|$. It is shown that for any measure preserving system $(X,\mathcal{X},μ,T)$ and any $f,g\in L^{\infty}(μ)$, the limit \begin{equation*} \lim_{N\to\infty}\frac{1}{N}\sum_{n=1}^{N}f(T^{\lfloor αn^c \rfloor}x)g(T^{\lfloor βn^c \rfloor}x) \end{equation*} exists for $μ$-a.e. $x\in X$. Meanwhile, a multidimensional version of the above result is also presented. |
| title | Pointwise convergence of double ergodic averages along certain non-polynomial sequences |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.17127 |