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A necessary and sufficient condition for Hardy's operator in
Authors:Farman I. Mamedov  Firana M. Mammadova
Affiliation:Institute Mathematics and Mechanics of Nat. Ac. Sci, Azerbaijan
Abstract:The equivalent conditions are proved for the Hardy inequality urn:x-wiley:dummy:mana201200291:equation:mana201200291-math-0002 to be fulfilled in the norms of a Lebesgue space with variable exponent urn:x-wiley:dummy:mana201200291:equation:mana201200291-math-0003. It is assumed that the function urn:x-wiley:dummy:mana201200291:equation:mana201200291-math-0004 is monotone and positive on (0, 1).
Keywords:The Hardy operator  variable exponent  weighted inequality  necessary and sufficient condition  42A05  42B25  26D10  35A2
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