Characterizes positive critical Hardy weights for Laplacians on weighted graphs and identifies an optimal Hardy weight for fractional Laplacians under suitable assumptions, with examples on Cayley, curvature, and fractal graphs.
Volume doubling, P oincar\'e inequality and G aussian heat kernel estimate for non-negatively curved graphs
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Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians
Characterizes positive critical Hardy weights for Laplacians on weighted graphs and identifies an optimal Hardy weight for fractional Laplacians under suitable assumptions, with examples on Cayley, curvature, and fractal graphs.