Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.06555 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912113237164032 |
|---|---|
| author | Bui, The Anh Zheng, Linfei |
| author_facet | Bui, The Anh Zheng, Linfei |
| contents | Let $L$ be a closed, densely defined operator on $L^2(\mathbb{R}^n)$ satisfying suitable $L^p-L^q$ off-diagonal estimates of order $κ> 0$. This paper aims to investigate the two-weight estimate and the Bloom weighted estimate for the fractional operator $L^{-α/κ}$ with $0 < α< n$ through the method of sparse domination. Our assumptions on the operators are minimal, and our result applies to a wide range of differential operators. As a byproduct, we also establish a new sparse domination criterion for a general class of fractional operators, including the classical fractional integral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Sparse Domination and Weighted Estimates for Fractional Operators Beyond Calderón-Zygmund Theory Bui, The Anh Zheng, Linfei Classical Analysis and ODEs Let $L$ be a closed, densely defined operator on $L^2(\mathbb{R}^n)$ satisfying suitable $L^p-L^q$ off-diagonal estimates of order $κ> 0$. This paper aims to investigate the two-weight estimate and the Bloom weighted estimate for the fractional operator $L^{-α/κ}$ with $0 < α< n$ through the method of sparse domination. Our assumptions on the operators are minimal, and our result applies to a wide range of differential operators. As a byproduct, we also establish a new sparse domination criterion for a general class of fractional operators, including the classical fractional integral. |
| title | New Sparse Domination and Weighted Estimates for Fractional Operators Beyond Calderón-Zygmund Theory |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.06555 |