A characterization of the harmonic bloch space and the harmonic besov spaces by an oscillation
| Autor: | Rikio Yoneda |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2002 |
| Předmět: | |
| Zdroj: | Proceedings of the Edinburgh Mathematical Society. Ser. 2. 45:229-239 |
| ISSN: | 0013-0915 |
| Popis: | We characterize the Bloch space and the Besov spaces of harmonic functions on the open unit disc $D$ by using the following oscillation:$$ \sup_\{\beta(z,w)\ltr\}(1-|z|^2)^{\alpha}(1-|w|^2)^{\beta}\biggl|\frac{\hat{D}^{(n-1)}h(z)-\hat{D}^{(n-1)}h(w)}{z-w}\biggr|, $$where $\alpha+\beta=n$, $\alpha,\beta\in\mathbb{R}$ and $\displaystyle{\hat{D}^{(n)}=(\partial^{n}/\partial^{n}z+\partial^{n}/\partial^{n}\bar{z})}$.AMS 2000 Mathematics subject classification: Primary 46E15 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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