Besicovitch-weighted ergodic theorems with continuous time
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910781796253696 |
|---|---|
| author | Litvinov, Semyon |
| author_facet | Litvinov, Semyon |
| contents | Given $1\leq p<\infty$, we show that ergodic flows in the $L^p$-space over a $σ$-finite measure space generated by strongly continuous semigroups of Dunford-Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly (in Egorov's sense). The corresponding local ergodic theorem is proved with identification of the limit. Then we extend these results to arbitrary fully symmetric spaces, including Orlicz, Lorentz, and Marcinkiewicz spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Besicovitch-weighted ergodic theorems with continuous time Litvinov, Semyon Dynamical Systems Functional Analysis Given $1\leq p<\infty$, we show that ergodic flows in the $L^p$-space over a $σ$-finite measure space generated by strongly continuous semigroups of Dunford-Schwartz operators and modulated by bounded Besicovitch almost periodic functions converge almost uniformly (in Egorov's sense). The corresponding local ergodic theorem is proved with identification of the limit. Then we extend these results to arbitrary fully symmetric spaces, including Orlicz, Lorentz, and Marcinkiewicz spaces. |
| title | Besicovitch-weighted ergodic theorems with continuous time |
| topic | Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2501.02606 |