Complex Interpolation and the Monotonicity in the Spatial Integrability Parameter of Exponentially Weighted Modulation Spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929723242708992 |
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| author | Chaichenets, Leonid Hausmann, Jan |
| author_facet | Chaichenets, Leonid Hausmann, Jan |
| contents | We introduce the notion of common retraction and coretraction for families of Banach spaces, formulate a framework for identifying interpolation spaces, and apply it to modulation spaces with exponential weights $E^s_{p,q}$. By constructing the domain of the common coretraction, we are able to prove $E^s_{o, q} \hookrightarrow E^s_{p, q}$ for $o \leq p$, i.e. the monotonicity in the spatial integrability parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00797 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complex Interpolation and the Monotonicity in the Spatial Integrability Parameter of Exponentially Weighted Modulation Spaces Chaichenets, Leonid Hausmann, Jan Functional Analysis Analysis of PDEs We introduce the notion of common retraction and coretraction for families of Banach spaces, formulate a framework for identifying interpolation spaces, and apply it to modulation spaces with exponential weights $E^s_{p,q}$. By constructing the domain of the common coretraction, we are able to prove $E^s_{o, q} \hookrightarrow E^s_{p, q}$ for $o \leq p$, i.e. the monotonicity in the spatial integrability parameter. |
| title | Complex Interpolation and the Monotonicity in the Spatial Integrability Parameter of Exponentially Weighted Modulation Spaces |
| topic | Functional Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2410.00797 |