Non-zero functions exist in L_{p,q}(R^d) with Fourier transform supported on a set of zero (2d/p, β)-Netrusov-Hausdorff capacity if and only if β > q/(2(q-1)).
Dobronravov,Frostman lemma revisited, Annales Fennici Mathematici, 49(1) (2024), 303-318
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Uncertainty Principle for distributions with Fourier transform in $L_{p,q}(\mathbb{R}^d)$
Non-zero functions exist in L_{p,q}(R^d) with Fourier transform supported on a set of zero (2d/p, β)-Netrusov-Hausdorff capacity if and only if β > q/(2(q-1)).