Frostman lemma revisited

Publication date: 21 April 2022

Abstract: 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

(p a r t i a l_{1}^{m_{1}} f, p a r t i a l_{2}^{m_{2}} f, l d o t s, p a r t i a l_{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.

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