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arXiv · 2509.26338

Carleson Measures, Vanishing Mean Oscillation and Critical Points

Carlo Bellavita·Artur Nicolau·Georgios Stylogiannis
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Abstract

Given a finite positive Borel measure $\mu$ in the open unit disc of the complex plane, we construct a bounded outer function $E$ whose boundary values have vanishing mean oscillation such that $|E| \mu$ is a vanishing Carleson measure. As an application it is shown that given any function in a Hardy space, there exists a bounded analytic function in the unit disc whose boundary values have vanishing mean oscillation, with the same critical points and multiplicities.

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Carlo Bellavita, Artur Nicolau, Georgios Stylogiannis. 2025-09-30. Carleson Measures, Vanishing Mean Oscillation and Critical Points. https://arxiv.org/abs/2509.26338

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