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arXiv · 2008.04494

Cwikel-Solomyak estimates on tori and Euclidean spaces

Fedor Sukochev·Dmitriy Zanin
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Abstract

We revise Cwikel-type estimate for the singular values of the operator $(1-Δ_{\mathbb{T}^d})^{-\frac{d}{4}}M_f(1-Δ_{\mathbb{T}^d})^{-\frac{d}{4}}$ on the torus $\mathbb{T}^d$ for the ideal $\mathcal{L}_{1,\infty}$, established by M.Z. Solomyak in even dimensions in \cite{Solomyak1995}, and extend it to odd dimensions. We obtain a new result for (symmetrized) Cwikel type estimates for Laplacians on $\mathbb{R}^d$ for arbitrary positive integer $d.$

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Fedor Sukochev, Dmitriy Zanin. 2020-08-11. Cwikel-Solomyak estimates on tori and Euclidean spaces. https://arxiv.org/abs/2008.04494

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