Bounds for Hardy type differences

Let A _k be an integral operator defined by

$ A_k f\left( x \right) = \frac{1} {{K\left( x \right)}}\int_{\Omega _2 } {k\left( {x,y} \right)f\left( y \right)d\mu _2 \left( y \right),} $ A_k f\left( x \right) = \frac{1} {{K\left( x \right)}}\int_{\Omega _2 } {k\left( {x,y} \right)f\left( y \right)d\mu _2 \left( y \right),}
Keywords:	Inequalities  Hardy inequality  Hilbert inequality  Hardy type inequalities
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