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Math. Inequal. Appl., 2014, Volume 17, Issue 3, Pages 879–898 (Mi mia3)  

Weighted Hardy-type inequalities on the cone of quasi-concave functions

L.-E. Perssonab, O. V. Popovac, V. D. Stepanovc

a Lulea Univ Technol, Dept Engn Sci & Math, SE-97187 Lulea, Sweden
b Narvik Univ, NO-8505 Narvik, Norway
c Peoples Friendship Univ Russia, Dept Math Anal & Funct Theory, Moscow 117198, Russia

Abstract: 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 $q\geqslant1$, $p>0$ and sufficient conditions for the rest of the range of parameters.

DOI: https://doi.org/10.7153/mia-17-64


Bibliographic databases:

MSC: 39B62, 45P05
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