摘要
We consider the convolution transforms of measures on R<sup>d</sup> defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution function and the local Lipschitz exponent of the measure. In particular, the results can be applied to the Poisson and Gauss-Weierstrass kernels. We can then obtain some singular boundary behavior of positive harmonic or parabolic functions on R<sub>+</sub><sup>d+1</sup> by multifractal analysis of measures.
We consider the convolution transforms of measures on R<sup>d</sup> defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution function and the local Lipschitz exponent of the measure. In particular, the results can be applied to the Poisson and Gauss-Weierstrass kernels. We can then obtain some singular boundary behavior of positive harmonic or parabolic functions on R<sub>+</sub><sup>d+1</sup> by multifractal analysis of measures.
作者
Zhiying Wen, Department of Mathematics, Wuhan University, Wuhan 430072, P. R. China Department of Applied Mathematics, Tsinghua University, Beijing 100084, P. R. ChinaE-mail: wenzy@tsinghua.edu.cnYiping Zhang, Department of Mathematics, Wuhan University, Wuhan 430072, P. R. ChinaE-mail: ypzhang@whu.edu.cn
基金
Research supported by the NNSF of China
