A measure with small support and p-summable Fourier transform
We construct a probability measure $μ$ supported on a set of zero $2d/p$-Hausdorff measure such that $\hatμ\in L_{p}(\mathbb{R}^d)$.
math.CA↗
arXiv subjects
Nikita P. Dobronravov
Publications and source records attributed to Nikita P. Dobronravov.
Frostman lemma revisited
We study sharpness of various generalizations of Frostman's lemma. These generalizations provide better estimates for the lower Hausdorff dimension of measures. As a corollary, we prove that if a generalized anisotropic gradient $(\partial_1^{m_1} f, \partial_2^{m_2} f,\ldots, \partial_d^{m_d} f)$ of a function $f$ in $d$ variables is a measure of bounded variation, then this measure is absolutely continuous with respect to the Hausdorff $d-1$ dimensional measure.
math.CA↗