Geodesic
Lower bound of the supremum of ergodic averages for ${\mathbb{Z}^d}$ and ${\mathbb{R}^d}$-actions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 626-636

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For ergodic ${\mathbb{Z}^d}$ and ${\mathbb{R}^d}$-actions, we obtain a pointwise lower bound for the supremum of ergodic averages. For ${\mathbb{Z}^d}$-actions in the case when the supremum is taken over multi-indices exceeding $\vec{n}$ located in a certain sector, the resulting inequality is not improvable over $\vec{n}$ in the class of all averaging integrable functions.
Keywords: rates of convergence in ergodic theorems, individual ergodic theorem, Wiener–Wintner ergodic theorem. 
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     author = {I. V. Podvigin},
     title = {Lower bound of the supremum of ergodic averages for ${\mathbb{Z}^d}$ and ${\mathbb{R}^d}$-actions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {626--636},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a130/}
}
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I. V. Podvigin. Lower bound of the supremum of ergodic averages for ${\mathbb{Z}^d}$ and ${\mathbb{R}^d}$-actions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 626-636. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a130/