|
This article is cited in 1 scientific paper (total in 1 paper)
Weakly Outer Inner Functions
E. Doubtsov St. Petersburg State University, Department of Mathematics and Mechanics
Abstract:
An inner function $I$ in the unit ball $B_n\subset\mathbb{РЎ}^n$ is said to be weakly outer if the closed subspace $IH^p(B_n)$ is weakly dense in the Hardy space $H^p(B_n)$, $0<p<1$. We construct weakly outer inner functions in the ball $B_n$ for all $n\ge 1$. We also investigate inner functions $I$ such that the subspace $I H^p(B_n)$ is not weakly dense in $H^p(B_n)$.
Keywords:
Hardy class, pluriharmonic measure.
Received: 13.05.2002
Citation:
E. Doubtsov, “Weakly Outer Inner Functions”, Funktsional. Anal. i Prilozhen., 37:2 (2003), 7–15; Funct. Anal. Appl., 37:2 (2003), 86–93
Linking options:
https://www.mathnet.ru/eng/faa144https://doi.org/10.4213/faa144 https://www.mathnet.ru/eng/faa/v37/i2/p7
|
Statistics & downloads: |
Abstract page: | 396 | Full-text PDF : | 181 | References: | 72 |
|