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| SINGULAR BOUNDARY PROPERTIES OF HARMONICFUNCTIONS AND FRACTAL ANALYSIS |
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Citation： |
Wen Zhiying,Zhang Yiping.SINGULAR BOUNDARY PROPERTIES OF HARMONICFUNCTIONS AND FRACTAL ANALYSIS[J].Chinese Annals of Mathematics B,1997,18(3):337~344 |
| Page view： 1005
Net amount： 694 |
Authors： |
Wen Zhiying; Zhang Yiping |
Foundation： |
Project supported by the National Natural Science
Foundation of China |
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| Abstract： |
This paper shows an important relation between the fractal analysis
and the boundary properties of harmonic functions. It is proved that the
multifractal analysis of a finite measure $\mu$ on $\R^d$ determines
the (non-tangential) boundary increasing properties of $P\mu$, the Poisson
integral of $\mu$ which is harmonic on $\R_{+}^{d+1}$. Some examples are given. |
Keywords： |
Fractal, Harmonic function, Multifractal analysis |
Classification： |
31B25, 31C35 |
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