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.
The best constant in a fractional H ardy inequality
2 Pith papers cite this work. Polarity classification is still indexing.
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Equivalence of homogeneous L^p-Sobolev norms for Hardy operators with and without potential is established via new square function estimates for slowly decaying heat kernels.
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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.
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Equivalence of Sobolev norms in Lebesgue spaces for Hardy operators in a half-space
Equivalence of homogeneous L^p-Sobolev norms for Hardy operators with and without potential is established via new square function estimates for slowly decaying heat kernels.