Quantitative ergodic theorems for actions of groups of polynomial growth
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915726666760192 |
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| author | Hong, Guixiang Liu, Wei |
| author_facet | Hong, Guixiang Liu, Wei |
| contents | We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in this setting the quantitative ergodic theorem, in particular, the upcrossing inequalities with exponential decay. The ideas or techniques involve probability theory, non-doubling Calderón-Zygmund theory, almost orthogonality argument and some delicate geometric argument involving the balls and the cubes on the group equipped with a not necessarily doubling measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_02635 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quantitative ergodic theorems for actions of groups of polynomial growth Hong, Guixiang Liu, Wei Dynamical Systems Classical Analysis and ODEs We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in this setting the quantitative ergodic theorem, in particular, the upcrossing inequalities with exponential decay. The ideas or techniques involve probability theory, non-doubling Calderón-Zygmund theory, almost orthogonality argument and some delicate geometric argument involving the balls and the cubes on the group equipped with a not necessarily doubling measure. |
| title | Quantitative ergodic theorems for actions of groups of polynomial growth |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2104.02635 |