arXiv:2410.07773 [math.FA]AbstractReferencesReviewsResources
Potential theory and boundary behavior in the Drury-Arveson space
Nikolaos Chalmoukis, Michael Hartz
Published 2024-10-10Version 1
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.
Comments: 40 pages
Related articles: Most relevant | Search more
arXiv:1701.07777 [math.FA] (Published 2017-01-26)
Henkin measures for the Drury-Arveson space
arXiv:2204.01559 [math.FA] (Published 2022-04-04)
An invitation to the Drury-Arveson space
arXiv:1608.04325 [math.FA] (Published 2016-08-15)
Aleksandrov-Clark theory for the Drury-Arveson space