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Weighted Hardy Operators in Complementary Morrey Spaces
2012
Journal of Function Spaces and Applications
We study the weightedp→q-boundedness of the multidimensional weighted Hardy-type operatorsHwαandℋwαwith radial type weightw=w(|x|), in the generalized complementary Morrey spacesℒ∁{0}p,ψ(ℝn)defined by an almost increasing functionψ=ψ(r). We prove a theorem which provides conditions, in terms of some integral inequalities imposed onψandw, for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the functionψand the weightware
doi:10.1155/2012/283285
fatcat:as3vpdwx2bey7i6hum4njio2ba