Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2307.15259 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914935053746176 |
|---|---|
| author | Hults, Jennifer Reinhold-Larsson, Karin |
| author_facet | Hults, Jennifer Reinhold-Larsson, Karin |
| contents | $T$ is a Ritt operator in $L^p$ if $\sup_n n\|T^n-T^{n+1}\|<\infty$. From \cite{LeMX-Vq}, if $T$ is a positive contraction and a Ritt operator in $L^p$, $1<p<\infty$, the square function
$\left( \sum_n n^{2m+1} |T^n(I-T)^{m+1}f|^2 \right)^{1/2}$ is bounded. We show that if $T$ is a Ritt operator in $L^1$, \[Q_{α,s,m}f=\left( \sum_n n^α |T^n(I-T)^mf|^s \right)^{1/s}\] is bounded $L^1$ when $α+1<sm$, and examine related questions on variational and oscillation norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15259 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Square Functions for Ritt Operators in $L^1$ Hults, Jennifer Reinhold-Larsson, Karin Spectral Theory $T$ is a Ritt operator in $L^p$ if $\sup_n n\|T^n-T^{n+1}\|<\infty$. From \cite{LeMX-Vq}, if $T$ is a positive contraction and a Ritt operator in $L^p$, $1<p<\infty$, the square function $\left( \sum_n n^{2m+1} |T^n(I-T)^{m+1}f|^2 \right)^{1/2}$ is bounded. We show that if $T$ is a Ritt operator in $L^1$, \[Q_{α,s,m}f=\left( \sum_n n^α |T^n(I-T)^mf|^s \right)^{1/s}\] is bounded $L^1$ when $α+1<sm$, and examine related questions on variational and oscillation norms. |
| title | Square Functions for Ritt Operators in $L^1$ |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2307.15259 |