Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 22 (2015), No. 2, 553--568Copyright Heldermann Verlag 2015 Boundedness Criterions for the Hardy Operator in Weighted Lp(.)(0,l) Space Farman Mamedov Mathematics and Mechanics Institute, National Academy of Sciences, B. Vahabzade 9, Baku 1141, Azerbaijan farman-m@mail.ru Firana M. Mammadova Mathematics and Mechanics Institute, National Academy of Sciences, B. Vahabzade 9, Baku 1141, Azerbaijan mamedovafira@yahoo.com Mushviq Aliyev Mathematics and Mechanics Institute, National Academy of Sciences, B. Vahabzade 9, Baku 1141, Azerbaijan a.mushfiq@rambler.ru [Abstract-pdf] Equivalent conditions are proved for the Hardy type weighted inequality $$\Big\Vert W(\cdot)^{-1}\sigma(\cdot)^{\frac{1}{p(\cdot)}} \int_{0}^{x} f(t)dt \Big \Vert_{L^{p(\cdot)}(0,l)} \leq C \Big \Vert \omega(\cdot)^{ \frac{1}{p(\cdot)}} f \Big \Vert_{L^{p(\cdot)}(0,l)}, \; \; \; f \geq 0$$ to be fulfilled in the norms of a Lebesgue space with variable exponent $L^{p(.)}(0,l)$. It is assumed that the function $p(.)$ is a monotone function. Keywords: Hardy operator, Hardy type inequality, variable exponent, weighted inequality, necessary and sufficient condition. MSC: 42A05, 42B25, 26D10; 35A23 [ Fulltext-pdf  (161  KB)] for subscribers only.