一类单位逼近所定义的卷积函数的边界分形性质  

Some Boundary Fractal Properties of the ConvolutionTransform of Measures by an Approximate Identity

作　　者：文志英[1] 章逸平[1] 

机构地区：[1]武汉大学数学系

出　　处：《数学学报（中文版）》1998年第5期965-968,共4页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金

摘　　要：我们研究一类单位逼近与具有重分形分解的测度的卷积所定义的函数，给出测度的局部Ｌｉｐｓｃｈｉｔｚ指数与函数的奇异边界增长性质的关系．特别应用于Ｐｏｉｓｏｎ核和ＧａｕｓＷｅｉｅｒｓｔｒａｓ核。We consider the convolution transforms of measures on R d defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution and the local Lipschitz exponent of the measure. We can then obtain some singular boundary behaviour of positive harmonic or parabolicfunctions on R d+1 + by multifractal analysis of measures.

关 键 词：单位逼近 重分形 卷积函数 调和函数 热函数 

分 类 号：O174.12[理学—数学] O174.3[理学—基础数学]