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On a Conjecture of Kufner and Persson

Pankaj Jain,Pawan K. Jain,Babita Gupta

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS（2007）

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Abstract
The L-p-L-q boundedness of the (conjugate) Hardy operator (L* f) (x) = integral(infinity)(x) l(t, x)f(t) dt for the case 0 < q < 1 has been studied and thereby a conjecture of Kufner and Persson is proved. An important role here is played by level type functions.
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Key words
Hardy operator,conjugate Hardy operator,kernel,level functions,boundedness
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