### Weighted Orlicz-Type Integral Inequalities for the Hardy Operator

C. J. Neugebauer
Source: Real Anal. Exchange Volume 32, Number 2 (2006), 495-510.

#### Abstract

We study integral inequalities for the Hardy operator $Hf$ of the form $\int_0^\infty\Phi[Hf^p]\,d\mu\leq c_0\int_0^\infty\Phi[c_1f^p]\,d\mu$, where $\Phi$ is convex, $\mu$ is a measure on $\mathbb R_+$, $1\leq p < \infty$, and $f$ is non-increasing. The results we obtain are extensions of the classical $B_p-$ weight theory [1,5].

First Page:
Primary Subjects: 42B25, 42B35
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rae/1199377486
Mathematical Reviews number (MathSciNet): MR2369858
Zentralblatt MATH identifier: 1134.42009