Approximation in Hölder Spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917125867700224 |
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| author | Mudarra, Carlos Oikari, Tuomas |
| author_facet | Mudarra, Carlos Oikari, Tuomas |
| contents | We introduce new vanishing subspaces of the homogeneous Hölder space $\dot{C}^{0,ω}(X,Y)$ in the generality of a doubling modulus $ω$ and normed spaces $X$ and $Y.$ For many couples $X,Y,$ we show these vanishing subspaces to completely characterize those Hölder functions that admit approximations, in the Hölder seminorm, by smooth, Lipschitz and boundedly supported functions. We present connections to bi-parameter harmonic analysis on the Euclidean space by providing applications to the compactness of the bi-commutator of two Calderón-Zygmund operators |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_01695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation in Hölder Spaces Mudarra, Carlos Oikari, Tuomas Functional Analysis Classical Analysis and ODEs 41A29, 42B35, 42B37, 46T20, 26B35 We introduce new vanishing subspaces of the homogeneous Hölder space $\dot{C}^{0,ω}(X,Y)$ in the generality of a doubling modulus $ω$ and normed spaces $X$ and $Y.$ For many couples $X,Y,$ we show these vanishing subspaces to completely characterize those Hölder functions that admit approximations, in the Hölder seminorm, by smooth, Lipschitz and boundedly supported functions. We present connections to bi-parameter harmonic analysis on the Euclidean space by providing applications to the compactness of the bi-commutator of two Calderón-Zygmund operators |
| title | Approximation in Hölder Spaces |
| topic | Functional Analysis Classical Analysis and ODEs 41A29, 42B35, 42B37, 46T20, 26B35 |
| url | https://arxiv.org/abs/2401.01695 |