New equivalent conditions for Hardy-type inequalities

Abstract

We consider a Hardy-type inequality with Oinarov's kernel in weighted Lebesgue spaces. We give new equivalent conditions for satisfying the inequality, and provide lower and upper estimates for its best constant. The findings are crucial in the study of oscillation and non-oscillation properties of differential equation solutions, as well as spectral properties.

Keywords

• integral operator
• norm
• weight function
• lebesgue space
• hardy-type inequality
• kernel