Interpolation spaces of Besov hierarchical spaces and non-linearities defined by vertex K functional and grid topology
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910634267901952 |
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| author | Yang, Qixiang Yang, Haibo |
| author_facet | Yang, Qixiang Yang, Haibo |
| contents | In 1967, Peetre proposed to give a precise description of the real interpolation space for Besov hierarchical spaces $l^{s,q}(A)$. In 1974, Cwikel proved that the Lions-Peetre formula for $(l^{q_0}(A_0), l^{q_1}(A_1))_{θ,r}$ have no reasonable generalization for any $r\neq q$. In this paper, we apply wavelets to transform the study of real interpolation space into {\bf the study of nonlinear functional structure and nonlinear topological structure}. We solve completely Peetre's longstanding open problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpolation spaces of Besov hierarchical spaces and non-linearities defined by vertex K functional and grid topology Yang, Qixiang Yang, Haibo Functional Analysis 46B70, 46E35, 42B35 In 1967, Peetre proposed to give a precise description of the real interpolation space for Besov hierarchical spaces $l^{s,q}(A)$. In 1974, Cwikel proved that the Lions-Peetre formula for $(l^{q_0}(A_0), l^{q_1}(A_1))_{θ,r}$ have no reasonable generalization for any $r\neq q$. In this paper, we apply wavelets to transform the study of real interpolation space into {\bf the study of nonlinear functional structure and nonlinear topological structure}. We solve completely Peetre's longstanding open problem. |
| title | Interpolation spaces of Besov hierarchical spaces and non-linearities defined by vertex K functional and grid topology |
| topic | Functional Analysis 46B70, 46E35, 42B35 |
| url | https://arxiv.org/abs/2410.03670 |