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Weighted Hardy’s inequalities with mixed norm. II. (English) Zbl 1006.26015

Let \(k(x,y)\geq 0\) for \(y<x\) and define the operators \[ If(x)=\int_{-\infty}^xk(x,y)f(y) dy,\quad I^*f(x)=\int_x^\infty k(y,x)f(y) dy. \] The author finds conditions on the weights such that the operators \(I\) and \(I^*\) satisfy a weighted inequality. The first part was published in [RGMIA Res. Rep. Coll. 3, No. 1, (2000)].

MSC:

26D15 Inequalities for sums, series and integrals
26D10 Inequalities involving derivatives and differential and integral operators
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