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Weighted Hardy-type inequalities on the cone of quasi-concave functions. (English) Zbl 1291.39049

Summary: The paper is devoted to the study of weighted Hardy-type inequalities on the cone of quasi-concave functions, which is equivalent to the study of the boundedness of the Hardy operator between the Lorentz \(\Gamma \)-spaces. For described inequalities we obtain necessary and sufficient conditions to hold for parameters \(q\geq 1 , p > 0\) and sufficient conditions for the rest of the range of parameters.

MSC:

39B62 Functional inequalities, including subadditivity, convexity, etc.
45P05 Integral operators
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