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arXiv · 2506.08115

Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels

Krzysztof Bogdan·Konstantin Merz
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Abstract

Motivated by the study of relativistic atoms, we prove sharp heat kernel bounds for the Hardy operator $(-\Delta)^{\alpha/2}-\kappa|x|^{-\alpha}$ acting on functions of the form $u(|x|) |x|^{\ell} Y_{\ell,m}(x/|x|)$ in $L^2(\R^d)$, when $\alpha\in(0,2]\cap(0,d+2\ell)$.

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Krzysztof Bogdan, Konstantin Merz. 2025-06-09. Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels. https://arxiv.org/abs/2506.08115

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