Geodesic
Some characterizations of harmonic Bloch and Besov spaces
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 417-430
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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).
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).
DOI : 10.1007/s10587-016-0265-y
Classification : 30C20, 31B05, 32A18
Keywords: harmonic function; Bloch space; Besov space; majorant 
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Fu, Xi; Lu, Bowen. Some characterizations of harmonic Bloch and Besov spaces. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 417-430. doi: 10.1007/s10587-016-0265-y

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