Reverse Hardy-type inequalities for supremal operators with measures

Abstract

In this paper we characterize the validity of the inequalities $\Vert g{\Vert }_{p,(a,b),\lambda }\le c\Vert u(x)\Vert g{\Vert }_{\infty ,(x,b),\mu }{\Vert }_{q,(a,b),\nu }$ 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 $0<p\le +\infty$, $0<q\le +\infty$, $\lambda$, $\mu$ and $\nu$ are non-negative Borel measures on $(a,b)$, and $u$ is a weight function on $(a,b)$.

Accepted in Mathematical Inequalities & Applications

Cited by in corpus (1)

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