Boundary behavior of 𝐵𝑀𝑂(𝐵_{𝑛})

Russo, Paula A.

doi:10.1090/S0002-9947-1985-0808751-8

Boundary behavior of $\textrm {BMO}(B_ n)$
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Trans. Amer. Math. Soc. 292 (1985), 733-740 Request permission

Abstract:

If $f$ is a holomorphic function of bounded mean oscillation in the unit ball of ${{\mathbf {C}}^n}$, then it has radial limits at almost every point of the boundary of the ball. The question remains as to how nicely one can expect this function to behave on subsets of the boundary of zero measure. For example, there is a holomorphic BMO function in the ball that has a finite radial limit at no point of the $n$-torus. We show here that this is not an isolated phenomenon; there exists at least one other $n$-dimensional submanifold of the boundary of the ball with this same behavior.

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