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arXiv · 2410.07773

Potential theory and boundary behavior in the Drury-Arveson space

Nikolaos Chalmoukis·Michael Hartz
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Abstract

We develop a notion of capacity for the Drury-Arveson space $H^2_d$ of holomorphic functions on the Euclidean unit ball. We show that every function in $H^2_d$ has a non-tangential limit (in fact Kor\'anyi limit) at every point in the sphere outside of a set of capacity zero. Moreover, we prove that the capacity zero condition is sharp, and that it is equivalent to being totally null for $H^2_d$. We also provide applications to cyclicity. Finally, we discuss generalizations of these results to other function spaces on the ball.

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Nikolaos Chalmoukis, Michael Hartz. 2024-10-10. Potential theory and boundary behavior in the Drury-Arveson space. https://arxiv.org/abs/2410.07773

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