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arXiv · 2605.19423

Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians

Philipp Hake·Matthias Keller·Felix Pogorzelski
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Abstract

We characterize positive critical Hardy weights for general Laplacians on weighted graphs. We then apply this result to fractional Laplacians on general graphs and use the characterization to identify an optimal Hardy weight under suitable assumptions. We finally illustrate our results with examples of graphs which arise as Cayley graphs of groups, satisfy curvature assumptions or are fractal graphs.

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Philipp Hake, Matthias Keller, Felix Pogorzelski. 2026-05-19. Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians. https://arxiv.org/abs/2605.19423

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