Weighted Hardy Operators in Complementary Morrey Spaces
2012 ◽
Vol 2012
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pp. 1-19
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Keyword(s):
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 power functions. We also prove that the spacesℒ∁{0}p,ψ(Ω)over bounded domains Ω are embedded between weighted Lebesgue spaceLpwith the weightψand such a space with the weightψ, perturbed by a logarithmic factor. Both the embeddings are sharp.
2021 ◽
Vol 24
(6)
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pp. 1643-1669
Keyword(s):
Keyword(s):
2010 ◽
Vol 5
(3)
◽
pp. 531-539
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Keyword(s):
2001 ◽
Vol 83
(2)
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pp. 390-418
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