Fractional Leibniz rules for the Dunkl Laplacian in Besov and Triebel--Lizorkin spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914612512817152 |
|---|---|
| author | Bui, The Anh Han, Xueting Mukherjee, Suman |
| author_facet | Bui, The Anh Han, Xueting Mukherjee, Suman |
| contents | Let $L$ be the Dunkl Laplacian on the Euclidean space $\mathbb{R}^N$ associated with a normalized root system $R$ and a multiplicity function $k(ν)\geq 0$, $ν\in R$. We establish a Leibniz-type rule for the fractional powers of $L$ on Besov and Triebel--Lizorkin spaces in the Dunkl setting. Our approach exploits the interplay between spectral multipliers and the Dunkl transform, together with the support properties of the distributions associated with Dunkl translations. These results extend the corresponding Leibniz-type estimates previously established on $L^p$ spaces to the broader setting of Besov and Triebel--Lizorkin spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29406 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fractional Leibniz rules for the Dunkl Laplacian in Besov and Triebel--Lizorkin spaces Bui, The Anh Han, Xueting Mukherjee, Suman Analysis of PDEs Classical Analysis and ODEs Functional Analysis 42B35, 42B25, 26A33, 44A15 Let $L$ be the Dunkl Laplacian on the Euclidean space $\mathbb{R}^N$ associated with a normalized root system $R$ and a multiplicity function $k(ν)\geq 0$, $ν\in R$. We establish a Leibniz-type rule for the fractional powers of $L$ on Besov and Triebel--Lizorkin spaces in the Dunkl setting. Our approach exploits the interplay between spectral multipliers and the Dunkl transform, together with the support properties of the distributions associated with Dunkl translations. These results extend the corresponding Leibniz-type estimates previously established on $L^p$ spaces to the broader setting of Besov and Triebel--Lizorkin spaces. |
| title | Fractional Leibniz rules for the Dunkl Laplacian in Besov and Triebel--Lizorkin spaces |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis 42B35, 42B25, 26A33, 44A15 |
| url | https://arxiv.org/abs/2605.29406 |