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arXiv · 2009.14112

On the sharpness of embeddings of H\"older spaces into Gaussian Besov spaces

Stefan Geiss
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Abstract

For an interpolation pair $(E_0,E_1)$ of Banach spaces with $E_1 \hookrightarrow E_0$ we use vectors $b_1,b_2,\ldots \in E_1$ that satisfy an extremal property with respect to the $J$- and $K$-functional to construct sub-spaces that are isometric to $\ell_q^{(\theta)}$. The construction is based on a randomisation using independent Rademacher variables. We verify that systems obtained by re-scaling a function with a certain periodicity property share this extreme property. This implies the sharpness of natural embeddings of H\"older spaces obtained by the real interpolation into the corresponding Gaussian Besov spaces.

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Stefan Geiss. 2020-09-29. On the sharpness of embeddings of H\"older spaces into Gaussian Besov spaces. https://arxiv.org/abs/2009.14112

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