位势型算子的加权不等式

Weighted Norm Inequalities for Potential Type Operators

中文关键词:  位势型算子  权函数  极大函数.

英文关键词:potential type operators  weight  maximal function.

中文摘要:

      设$\Phi$为${\mathbb{R}}^n$上的非负局部可积函数且满足弱增长条件, 位势型算子$T_{\Phi}$定义为$$T_{\Phi}f(x)=\int_{{\mathbb{R}}^n} \Phi(x-y)f(y)\dy.$$ 本文给出了位势型算子$T_{\Phi}$的几个强型与弱型加权不等式.

英文摘要:

      Let $\Phi$ be a non-negative locally integrable function on ${\mathbb{R}}^n$ and satisfy some weak growth conditions, define the potential type operator $T_{\Phi}$ by $$T_{\Phi}f(x)=\int_{{\mathbb{R}}^n} \Phi(x-y)f(y)\d y.$$ The aim of this paper is to give several strong type and weak type weighted norm inequalities for the potential type operator $T_{\Phi}$.