Polynomial ergodic theorems in the spirit of Dunford and Zygmund
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918326187327488 |
|---|---|
| author | Kosz, Dariusz Langowski, Bartosz Mirek, Mariusz Plewa, Paweł |
| author_facet | Kosz, Dariusz Langowski, Bartosz Mirek, Mariusz Plewa, Paweł |
| contents | The main goal of the paper is to prove convergence in norm and pointwise almost everywhere on $L^p$, $p\in (1,\infty)$, for certain multiparameter polynomial ergodic averages in the spirit of Dunford and Zygmund for continuous flows. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of uniform oscillation estimates for multiparameter polynomial Radon averaging operators. In the proof of our main result we develop flexible Fourier methods that exhibit and handle the so-called "parameters-gluing'' phenomenon, an obstruction that arises in studying oscillation and variation inequalities for multiparameter polynomial Radon operators. We will also discuss connections of our main result with a multiparameter variant of the Bellow-Furstenberg problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03802 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polynomial ergodic theorems in the spirit of Dunford and Zygmund Kosz, Dariusz Langowski, Bartosz Mirek, Mariusz Plewa, Paweł Dynamical Systems Classical Analysis and ODEs 37A30, 37A46, 42A45, 42A85, 43A25 The main goal of the paper is to prove convergence in norm and pointwise almost everywhere on $L^p$, $p\in (1,\infty)$, for certain multiparameter polynomial ergodic averages in the spirit of Dunford and Zygmund for continuous flows. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of uniform oscillation estimates for multiparameter polynomial Radon averaging operators. In the proof of our main result we develop flexible Fourier methods that exhibit and handle the so-called "parameters-gluing'' phenomenon, an obstruction that arises in studying oscillation and variation inequalities for multiparameter polynomial Radon operators. We will also discuss connections of our main result with a multiparameter variant of the Bellow-Furstenberg problem. |
| title | Polynomial ergodic theorems in the spirit of Dunford and Zygmund |
| topic | Dynamical Systems Classical Analysis and ODEs 37A30, 37A46, 42A45, 42A85, 43A25 |
| url | https://arxiv.org/abs/2304.03802 |