关于平方函数的Lip_α(R^n)有界性(0<α<1)

Boundness of the Square Function on Lip_α(R^n) (0<α<1)

本文利用向量值函数的方法,讨论了平方函数的Lip_。(R^n)性质,得到了以下结果:设T为一平方函数,尸f正Lip_。(R^n),若T(f)在某点处有限,则T(f)就几乎处处有限,且有‖Tf‖/f。≤c‖f‖加.本文的结果部分地改进了文[4]中的结论.

In this paper, we use the method of vector-valued function to study the behaviours of square functions when f∈Lipα(Rn) (0<α<1). Let T stand for a square function, we have following result: for f∈Lipα(Rn), if T(f) is finite at one point, then T(f) is finite in Rn except a set of zero measure and T(f) is a Lipschitz function (||Tf||Aα≤c||f||Aα). Our result improve the one of Yu Maohe ([4]) to some extents.