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arXiv · 2401.01695

Approximation in H\"older Spaces

Carlos Mudarra·Tuomas Oikari
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Abstract

We introduce new vanishing subspaces of the homogeneous H\"{o}lder space $\dot{C}^{0,\omega}(X,Y)$ in the generality of a doubling modulus $\omega$ and normed spaces $X$ and $Y.$ For many couples $X,Y,$ we show these vanishing subspaces to completely characterize those H\"older functions that admit approximations, in the H\"{o}lder 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 Calder\'on-Zygmund operators

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Carlos Mudarra, Tuomas Oikari. 2024-01-03. Approximation in H\"older Spaces. https://doi.org/10.1016/j.aim.2025.110634

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