Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T09:11:18.591Z Has data issue: false hasContentIssue false
  • English
  • Français

A CHARACTERIZATION OF THE HARMONIC BLOCH SPACE AND THE HARMONIC BESOV SPACES BY AN OSCILLATION

Published online by Cambridge University Press:  05 February 2002

Rikio Yoneda
Rikio Yoneda
Affiliation:
Tokyo Metropolitan College of Technology, Tokyo 140-0011, Japan (yoneda@tokyo-tmct.ac.jp)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Keywords

harmonic Bloch spaceharmonic Besov spaceoscillation
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 229 - 239
Copyright
Copyright © Edinburgh Mathematical Society 2002