Abstract:We establish necessary and sufficient conditions on a weight pair (v, w) governing the boundedness of the Riesz potential operatoris the Lebesgue space defined for non-negative radially decreasing functions on G. The same problem is also studied for the potential operator with product kernels I α 1 ,α 2 defined on a product of two homogeneous groups G 1 × G 2 . In the latter case weights, in general, are not of product type. The derived results are new even for Euclidean spaces. To get the main results we use … Show more
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