The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (190 KB) | Metadata | Table of Contents | ZAA summary
Volume 31, Issue 1, 2012, pp. 55–74
DOI: 10.4171/ZAA/1448

Published online: 2011-12-27

On equivalent conditions for the general weighted Hardy type inequality in space $L^{p(\cdot)}$

Farman I. Mamedov[1] and Yusuf Zeren[2]

(1) National Academy of Sciences, Baku, Azerbaidjan
(2) Yildiz Technical University, Besiktas-Istanbul, Turkey

We study the Hardy type two-weighted inequality for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^{n})$. In this way we prove equivalent conditions for $L^{p(\cdot)}\rightarrow L^{q(\cdot)}$ boundedness of Hardy operator in the case of exponents $q(0)\geq p(0)$, $q(\infty)\geq p\left(\infty \right)$. We also prove that the condition for such inequality to hold coincides with condition for validity of two weighted Hardy inequalities with constant exponents, if we require the exponents to be regular near zero and at infinity.

Keywords: Hardy operator, Hardy inequality, variable exponents, weighted inequality

Mamedov Farman, Zeren Yusuf: On equivalent conditions for the general weighted Hardy type inequality in space $L^{p(\cdot)}$. Z. Anal. Anwend. 31 (2012), 55-74. doi: 10.4171/ZAA/1448