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| THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES |
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Citation： |
BU Shangquan.THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES[J].Chinese Annals of Mathematics B,2001,22(4):513~518 |
| Page view： 1166
Net amount： 930 |
Authors： |
BU Shangquan; |
Foundation： |
Project supported by the National Natural Science Foundation of China. |
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| Abstract： |
Let $X$ be a complex Banach space without
the analytic Radon-Nikodym property. The author shows that
$G = \{ f\in \h : \ \text{there \ exists}\ \epsilon > 0, \ \text{suchthat\ for}\ \text{almost\ all}\ \theta\in \0,\ \limsup\rs\limits \V f(\r ) - f(\s )\V \geq \epsilon\ \}$
is a dense open subset of $\h$. It is also shown that for every
open subset $B$ of $\T$, there exists
$F\in \h$, such that $F$ has boundary values everywhere
on $B^c$ and $F$ has radial limits nowhere on $B$. When $A$ is a
measurable subset of $\T$ with positive measure, there exists $f\in \h$,
such that $f$ has nontangential limits almost
everywhere on $A^c$ and $f$ has radial limits almost nowhere on $A$. |
Keywords： |
Analytic Radon-Nikodym property, Radial limits and vector-valued
Hardy space |
Classification： |
46B20, 46B25 |
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