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Sufficient and necessary conditions of (L1, Lq)-boundedness for Hardy operator with power weight
Received date: 2013-03-01
Revised date: 2013-04-24
Online published: 2013-11-15
We characterize the sufficient and necessary conditions with respect to α and β which make the Hardy operator Hn and the Hardy operator's conjugate operator Hn* be bounded from L|x|α1(Rn) to L|x|βq( R n) with 1≤q<∞ in n-dimensional Euclidean spaces, respectively.
Key words： Hardy operator; conjugate operator; power weight; endpoint estimates
NIE Xu-Dong , WANG Shi-Mo , YAN Dun-Yan . Sufficient and necessary conditions of (L1, Lq)-boundedness for Hardy operator with power weight[J]. Journal of University of Chinese Academy of Sciences, 2013 , 30(6) : 724 -727 . DOI: 10.7523/j.issn.2095-6134.2013.06.002
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