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arXiv · 1606.08082

Besov spaces via hyperbolic fillings

Tomás Soto
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Abstract

We establish a new characterization of the homogeneous Besov spaces $\dot{\mathcal B}^{s}_{p,q}(Z)$ with smoothness $s \in (0,1)$ in the setting of doubling metric measure spaces $(Z,d,\mu)$. The characterization is given in terms of a hyperbolic filling of the metric space $(Z,d)$, a construction which has previously appeared in the context of other function spaces in [3,1,2]. We use the characterization to obtain results concerning the density of Lipschitz functions in the spaces $\dot{\mathcal B}^{s}_{p,q}(Z)$ and a general complex interpolation formula in the smoothness range $0 < s < 1$.

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Tomás Soto. 2016-06-26. Besov spaces via hyperbolic fillings. https://arxiv.org/abs/1606.08082

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