Potential theory and boundary behavior in the Drury-Arveson space

2024/10/10 by Nikolaos Chalmoukis, Chalmoukis, Nikolaos, Michael Hartz +1
Computer Science · Engineering · #32U20 #Complex Variables (math.CV) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Functional Analysis (math.FA) #Heat and Mass Transfer in Porous Media #Hydraulic Fracturing and Reservoir Analysis #Primary 46E22 #Secondary 31B15

paper · pdf · doi:10.48550/arxiv.2410.07773

openalex publication_date 2024/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a notion of capacity for the Drury-Arveson space H²_d of holomorphic functions on the Euclidean unit ball. We show that every function in H²_d has a non-tangential limit (in fact Korányi 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 H²_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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