Some characterizations of harmonic Bloch and Besov spaces

Czechoslovak Mathematical Journal

Xi Fu¹  Bowen Lu² 

[1] Department of Mathematics, Shaoxing University, No. 508, West Huancheng Road, Shaoxing 312000, Zhejiang, P. R. China;School of International Business, Zhejiang International Studies University, No. 140, Wensan Road, Hangzhou 310012, Zhejiang, P. R. China

关键词: harmonic function;    Bloch space;    Besov space;    majorant;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

The relationship between weighted Lipschitz functions and analytic Bloch spaces has attracted much attention. In this paper, we define harmonic $\omega$-$\alpha$-Bloch space and characterize it in terms of $$\omega((1-|x|^2)^\beta(1-|y|^2)^{\alpha- \beta}) \Big| \frac{f(x)-f(y)}{x-y}\Big|$$ and $$\omega((1-|x|^2)^\beta(1-|y|^2)^{\alpha- \beta}) \Big| \frac{f(x)-f(y)}{|x|y-x'}\Big|$$ where $\omega$ is a majorant. Similar results are extended to harmonic little $\omega$-$\alpha$-Bloch and Besov spaces. Our results are generalizations of the corresponding ones in G. Ren, U. Kahler (2005).

【 授权许可】

Unknown