Pavla Hofmanová
A weighted inequality for the Hardy operator involving suprema

Comment.Math.Univ.Carolin. 57,3 (2016) 317-326.

Abstract:Let $u$ be a weight on $(0, \infty)$. Assume that $u$ is continuous on $(0, \infty)$. Let the operator $S_{u}$ be given at measurable non-negative function $\varphi$ on $(0, \infty)$ by $$ S_{u}\varphi (t)= \sup_{0< \tau\leq t}u(\tau)\varphi (\tau). $$ We characterize weights $v,w$ on $(0, \infty)$ for which there exists a positive constant $C$ such that the inequality $$ \left( \int_{0}^{\infty}[S_{u}\varphi (t)]^{q}w(t)\,dt\right)^{\frac 1q} \lesssim \left( \int_{0}^{\infty}[\varphi (t)]^{p}v(t)\,dt\right)^{\frac 1p} $$ holds for every $0

Keywords: Hardy operators involving suprema; weighted inequalities

DOI: DOI 10.14712/1213-7243.2015.167
AMS Subject Classification: 47G10 26D15

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