A noncommutative weak type maximal inequality for modulated ergodic averages with general weights
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914333282271232 |
|---|---|
| author | O'Brien, Morgan |
| author_facet | O'Brien, Morgan |
| contents | In this article, we prove a weak type $(p,p)$ maximal inequality, $1<p<\infty$, for weighted averages of a positive Dunford-Schwarz operator $T$ acting on a noncommutative $L_p$-space associated to a semifinite von Neumann algebra $\mathcal{M}$, with weights in $W_q$, where $\frac{1}{p}+\frac{1}{q}=1$. This result is then utilized to obtain modulated individual ergodic theorems with $q$-Besicovitch and $q$-Hartman sequences as weights. Multiparameter versions of these results are also investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_04466 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A noncommutative weak type maximal inequality for modulated ergodic averages with general weights O'Brien, Morgan Operator Algebras Dynamical Systems In this article, we prove a weak type $(p,p)$ maximal inequality, $1<p<\infty$, for weighted averages of a positive Dunford-Schwarz operator $T$ acting on a noncommutative $L_p$-space associated to a semifinite von Neumann algebra $\mathcal{M}$, with weights in $W_q$, where $\frac{1}{p}+\frac{1}{q}=1$. This result is then utilized to obtain modulated individual ergodic theorems with $q$-Besicovitch and $q$-Hartman sequences as weights. Multiparameter versions of these results are also investigated. |
| title | A noncommutative weak type maximal inequality for modulated ergodic averages with general weights |
| topic | Operator Algebras Dynamical Systems |
| url | https://arxiv.org/abs/2302.04466 |