Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball. (English) Zbl 1513.31005
Summary: We consider harmonic Bergman-Besov spaces \(b^p_\alpha\) and weighted Bloch spaces \(b^\infty_\alpha\) on the unit ball of \(\mathbb{R}^n\) for the full ranges of parameters \(0<p<\infty\), \(\alpha\in\mathbb{R}\), and determine the precise inclusion relations among them. To verify these relations we use Carleson measures and suitable radial differential operators. For harmonic Bergman spaces various characterizations of Carleson measures are known. For weighted Bloch spaces we provide a characterization when \(\alpha>0\).
MSC:
| 31B05 | Harmonic, subharmonic, superharmonic functions in higher dimensions |
| 42B35 | Function spaces arising in harmonic analysis |
Keywords:
harmonic Bergman-Besov space; weighted harmonic Bloch space; Carleson measure; Berezin transformReferences:
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