Matrix weighted modulation spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909120223772672 |
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| author | Nielsen, Morten |
| author_facet | Nielsen, Morten |
| contents | Given a matrix-weight $W$ in the Muckenhoupt class $\mathbf{A}_p(\mathbb{R}^n)$, $1\leq p<\infty$, we introduce corresponding vector-valued continuous and discrete $α$-modulation spaces $M^{s,α}_{p,q}(W)$ and $m^{s,α}_{p,q}(W)$ and prove their equivalence through the use of adapted tight frames. Compatible notions of molecules and almost diagonal matrices are also introduced, and an application to the study of pseudo-differential operators on vector valued spaces is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16461 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matrix weighted modulation spaces Nielsen, Morten Functional Analysis Primary 42C40, 42C15, Secondary 42B15 Given a matrix-weight $W$ in the Muckenhoupt class $\mathbf{A}_p(\mathbb{R}^n)$, $1\leq p<\infty$, we introduce corresponding vector-valued continuous and discrete $α$-modulation spaces $M^{s,α}_{p,q}(W)$ and $m^{s,α}_{p,q}(W)$ and prove their equivalence through the use of adapted tight frames. Compatible notions of molecules and almost diagonal matrices are also introduced, and an application to the study of pseudo-differential operators on vector valued spaces is given. |
| title | Matrix weighted modulation spaces |
| topic | Functional Analysis Primary 42C40, 42C15, Secondary 42B15 |
| url | https://arxiv.org/abs/2402.16461 |