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arXiv · 1411.0645

Reverse Hardy-type inequalities for supremal operators with measures

R. Ch. Mustafayev·T. Ünver
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Abstract

In this paper we characterize the validity of the inequalities $\|g\|_{p,(a,b),λ} \le c \|u(x) \|g\|_{\infty,(x,b),μ}\|_{q,(a,b),ν}$ and $\label{eq.0.1.2} \|g\|_{p,(a,b),λ} \le c \|u(x) \|g\|_{\infty,(a,x),μ}\|_{q,(a,b),ν} $ for all non-negative Borel measurable functions $g$ on the interval $(a,b)$, where $0 < p \le +\infty$, $0 < q \le +\infty$, $λ$, $μ$ and $ν$ are non-negative Borel measures on $(a,b)$, and $u$ is a weight function on $(a,b)$.

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R. Ch. Mustafayev, T. Ünver. 2014-11-03. Reverse Hardy-type inequalities for supremal operators with measures. https://doi.org/10.7153/mia-18-101

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