Two-weight $L^p\to L^q$ bounds for positive dyadic operators in the case $0
Bibliographic Details
Title:
Two-weight $L^p\to L^q$ bounds for positive dyadic operators in the case $0
Authors:
Hänninen, Timo S., Verbitsky, Igor E.
Publication Year:
2017
Collection:
Mathematics
Subject Terms:
Mathematics - Classical Analysis and ODEs, 42B25, 42B35, 47G40
More Details:
Let $\sigma$, $\omega$ be measures on $\mathbb{R}^d$, and let $\{\lambda_Q\}_{Q\in\mathcal{D}}$ be a family of non-negative reals indexed by the collection $\mathcal{D}$ of dyadic cubes in $\mathbb{R}^d$. We characterize the two-weight norm inequality, \begin{equation*} \lVert T_\lambda(f\sigma)\rVert_{L^q(\omega)}\le C \, \lVert f \rVert_{L^p(\sigma)}\quad \text{for every $f\in L^p(\sigma)$,} \end{equation*} for the positive dyadic operator \begin{equation*} T_\lambda(f\sigma):= \sum_{Q\in \mathcal{D}} \lambda_Q \, \Big(\frac{1}{\sigma(Q)} \int_Q f\mathrm{d}\sigma\Big) \, 1_Q \end{equation*} in the difficult range $0
Document Type:
Working Paper
Access URL:
http://arxiv.org/abs/1706.08657
Accession Number:
edsarx.1706.08657
Database:
arXiv
| Title: | Two-weight $L^p\to L^q$ bounds for positive dyadic operators in the case $0 |
|---|---|
| Authors: | Hänninen, Timo S., Verbitsky, Igor E. |
| Publication Year: | 2017 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Classical Analysis and ODEs, 42B25, 42B35, 47G40 |
| More Details: | Let $\sigma$, $\omega$ be measures on $\mathbb{R}^d$, and let $\{\lambda_Q\}_{Q\in\mathcal{D}}$ be a family of non-negative reals indexed by the collection $\mathcal{D}$ of dyadic cubes in $\mathbb{R}^d$. We characterize the two-weight norm inequality, \begin{equation*} \lVert T_\lambda(f\sigma)\rVert_{L^q(\omega)}\le C \, \lVert f \rVert_{L^p(\sigma)}\quad \text{for every $f\in L^p(\sigma)$,} \end{equation*} for the positive dyadic operator \begin{equation*} T_\lambda(f\sigma):= \sum_{Q\in \mathcal{D}} \lambda_Q \, \Big(\frac{1}{\sigma(Q)} \int_Q f\mathrm{d}\sigma\Big) \, 1_Q \end{equation*} in the difficult range $0 |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/1706.08657 |
| Accession Number: | edsarx.1706.08657 |
| Database: | arXiv |
| Description not available. |