On Hardy spaces associated with the twisted Laplacian and sharp estimates for the corresponding wave operator
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909761173192704 |
|---|---|
| author | Basak, Riju Jotsaroop, K. |
| author_facet | Basak, Riju Jotsaroop, K. |
| contents | We prove various equivalent characterisations of the Hardy space $H^p_{\mathcal{L}}(\mathbb{C}^n)$ for $0<p<1$ associated with the twisted Laplacian $\mathcal{L}$ which generalises the result of [MPR81] for the case $p=1$. Using the atomic characterisation of $H^p_{\mathcal{L}}(\mathbb{C}^n)$ corresponding to the twisted convolution, we prove sharp boundedness result for the wave operator $\mathcal{L}^{-δ/2}e^{\pm it\sqrt{\mathcal{L}}}$ for a fixed $t>0$ on $H^p_{\mathcal{L}}(\mathbb{C}^n)$. More precisely we prove that it is a bounded operator from $H^p_{\mathcal{L}}(\mathbb{C}^n)$ to $L^p(\mathbb{C}^n)$ for $ 0<p\leq 1$ and $δ\geq (2n-1)\left(1/p-1/2\right)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Hardy spaces associated with the twisted Laplacian and sharp estimates for the corresponding wave operator Basak, Riju Jotsaroop, K. Functional Analysis Analysis of PDEs Classical Analysis and ODEs We prove various equivalent characterisations of the Hardy space $H^p_{\mathcal{L}}(\mathbb{C}^n)$ for $0<p<1$ associated with the twisted Laplacian $\mathcal{L}$ which generalises the result of [MPR81] for the case $p=1$. Using the atomic characterisation of $H^p_{\mathcal{L}}(\mathbb{C}^n)$ corresponding to the twisted convolution, we prove sharp boundedness result for the wave operator $\mathcal{L}^{-δ/2}e^{\pm it\sqrt{\mathcal{L}}}$ for a fixed $t>0$ on $H^p_{\mathcal{L}}(\mathbb{C}^n)$. More precisely we prove that it is a bounded operator from $H^p_{\mathcal{L}}(\mathbb{C}^n)$ to $L^p(\mathbb{C}^n)$ for $ 0<p\leq 1$ and $δ\geq (2n-1)\left(1/p-1/2\right)$. |
| title | On Hardy spaces associated with the twisted Laplacian and sharp estimates for the corresponding wave operator |
| topic | Functional Analysis Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.00327 |