A new scale of function spaces characterizing homogeneous Besov spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912753934925824 |
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| author | Auscher, Pascal Bechtel, Sebastian Haardt, Luca |
| author_facet | Auscher, Pascal Bechtel, Sebastian Haardt, Luca |
| contents | We introduce and study a new scale of function spaces that characterize the homogeneous Besov spaces $\mathrm{\dot B}^β_{p,q}$, hence completing earlier work by Ullrich. These new spaces include the ones introduced by Barton and Mayboroda, and systematically studied by Amenta under the name of weighted $\mathrm{Z}$-spaces, for the purpose of boundary value problems with $\mathrm{\dot B}^β_{p,p}$ data. They are the counterparts to the weighted tent spaces with Whitney averages, developed by Huang, and arise as their real interpolants. We describe their functional analytic properties: completeness, duality, embeddings, as well as their real and complex interpolants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_07399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new scale of function spaces characterizing homogeneous Besov spaces Auscher, Pascal Bechtel, Sebastian Haardt, Luca Classical Analysis and ODEs Functional Analysis 42B35, 46E30, 46B70 We introduce and study a new scale of function spaces that characterize the homogeneous Besov spaces $\mathrm{\dot B}^β_{p,q}$, hence completing earlier work by Ullrich. These new spaces include the ones introduced by Barton and Mayboroda, and systematically studied by Amenta under the name of weighted $\mathrm{Z}$-spaces, for the purpose of boundary value problems with $\mathrm{\dot B}^β_{p,p}$ data. They are the counterparts to the weighted tent spaces with Whitney averages, developed by Huang, and arise as their real interpolants. We describe their functional analytic properties: completeness, duality, embeddings, as well as their real and complex interpolants. |
| title | A new scale of function spaces characterizing homogeneous Besov spaces |
| topic | Classical Analysis and ODEs Functional Analysis 42B35, 46E30, 46B70 |
| url | https://arxiv.org/abs/2512.07399 |