Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.08409 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917426321424384 |
|---|---|
| author | Mukeshimana, Solange Rule, David |
| author_facet | Mukeshimana, Solange Rule, David |
| contents | Beltran \& Cladek~\cite{BC} use $L^r$ to $L^s$ bounds to prove sparse form bounds for pseudodifferential operators with Hörmander symbols in $S^m_{ρ,δ}$ up to, but not including, the sharp end-point in decay $m$. We further develop their technique, obtaining pointwise sparse bounds for rough pseudodifferential operators that are merely measurable in their spatial variables and an alternative proof of their results which avoids proving geometrically decaying sparse bounds. We also provide sufficient conditions for sparse form bounds to hold and use these to reprove know sparse bounds for pseudodifferential operators with symbols in $S^0_{1,δ}$ for $δ< 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some More Sparse Bounds for Rough and Smooth Pseudodifferential Operators Mukeshimana, Solange Rule, David Classical Analysis and ODEs Analysis of PDEs 35S05, 42B25 Beltran \& Cladek~\cite{BC} use $L^r$ to $L^s$ bounds to prove sparse form bounds for pseudodifferential operators with Hörmander symbols in $S^m_{ρ,δ}$ up to, but not including, the sharp end-point in decay $m$. We further develop their technique, obtaining pointwise sparse bounds for rough pseudodifferential operators that are merely measurable in their spatial variables and an alternative proof of their results which avoids proving geometrically decaying sparse bounds. We also provide sufficient conditions for sparse form bounds to hold and use these to reprove know sparse bounds for pseudodifferential operators with symbols in $S^0_{1,δ}$ for $δ< 1$. |
| title | Some More Sparse Bounds for Rough and Smooth Pseudodifferential Operators |
| topic | Classical Analysis and ODEs Analysis of PDEs 35S05, 42B25 |
| url | https://arxiv.org/abs/2507.08409 |