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《Journal of Jiangxi Normal University(Natural Science Edition)》 2018-03
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The Simple Proof of a Special Class of Caffarelli-Kohn-Nirenberg Inequality

LIU Min;ZHONG Xuexiu;School of Sciences,Liaoning Shihua University;School of Mathematical Sciences,Beijing Normal University;Department of Mathematics,Sun Yat-sen University;  
Some results about the well known Caffarelli-Kohn-Nirenberg inequality are reviewed. And a simple proof of the following special CKN inequality∫_(RN)|u|~p/|x|~(p(1+t))dx≤(p/(N-p-pt))~p∫_(RN)|▽u|~p/|x|~(pt)dx,u∈C∞c(R~N\{0})is given by using the Emden-Fowler transformation,where 2 ≤ p ∞,p(1 + t) N,and(p/(N-p-pt))~p is the best constant.
【Fund】: 国家自然科学基金(11701248)资助项目
【CateGory Index】: O178
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