\(p\)-Bloch space, \(Q_{p,0}\) space and holomorphic functions with Hadamard gap. (Chinese. English summary) Zbl 1020.32004
Summary: The relation between \(p\)-Bloch space \(B^p\) and \(Q_{p,0}\)-space is discussed by means of \(p\)-Carleson measure and holomorphic functions with Hadamard gaps.
The main results are: (1) If \({3\over 4}\leq p< 1\), then \(B^p\subset\bigcup_{1-{2(1-p)\over n}< q\leq 1} Q_{q,0}\), and the inclusion is proper; (2) Let \({n-1\over n}< q\leq 1- 2{2(1-p)\over n}\leq 1\), then \(B^p\) and \(Q_q\) can not include each other.
The main results are: (1) If \({3\over 4}\leq p< 1\), then \(B^p\subset\bigcup_{1-{2(1-p)\over n}< q\leq 1} Q_{q,0}\), and the inclusion is proper; (2) Let \({n-1\over n}< q\leq 1- 2{2(1-p)\over n}\leq 1\), then \(B^p\) and \(Q_q\) can not include each other.
MSC:
| 32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
