N. Dobronravov

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20222026

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math.CA2026

Besicovitch's covering theorem in the parabolic metric

Nikita Dobronravov

We prove that Besicovitch's covering theorem holds for the parabolic metric $d_{p} ((x_{1}, t_{1}), (x_{2}, t_{2})) = (∣ x_{1} - x_{2} ∣^{p} + ∣ t_{1} - t_{2} ∣^{\frac{p}{2}})^{\frac{1}{p}}$ on $\mathbb{R}^n\times\…

math.CA2026

Uncertainty Principle for distributions with Fourier transform in $L_{p, q} (R^{d})$

Nikita Dobronravov

A version of the Uncertainty Principle says: There does not exist a non zero function in $L_{p} (R^{d})$ if its Fourier transform is supported by a set of finite $α$ -Hausdorff…

math.CA2024

A measure with small support and p-summable Fourier transform

Nikita P. Dobronravov

We construct a probability measure $μ$ supported on a set of zero $2 d / p$ -Hausdorff measure such that $μ^\in L_{p} (R^{d})$ .

math.CA2022

Frostman lemma revisited