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Article

MSC: 30C20, 31B05, 32A18
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Keywords:
harmonic function; Bloch space; Besov space; majorant
Summary:
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. Kähler (2005).
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