Weighted Norm Inequalities for Potential Type Operators
Received:July 24, 2007  Revised:November 22, 2007
Key Word: potential type operators   weight   maximal function.  
Fund ProjectL:the Natural Science Foundation of Hebei Province (No.08M001) and the National Natural Science Foundation of China (Nos.10771049,60773174).
Author NameAffiliation
LI Wen Ming College of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China 
QI Jin Yun Department of Mathematics, Langfang Normal College, Hebei 065000, China 
YAN Xue Fang College of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China 
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Abstract:
      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 $T_{\Phi}$.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.05.016
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