Iterated discrete Hardy-type inequalities with three weights for a class of matrix operators

Abstract

Iterated Hardy-type inequalities are one of the main objects of current research on the theory of Hardy inequalities. These inequalities have become well-known after study boundedness properties of the multidimensional Hardy operator acting from the weighted Lebesgue space to the local Morrie-type space. In addition, the results of quasilinear inequalities can be applied to study bilinear Hardy inequalities. In the paper, we discussed weighted discrete Hardy-type inequalities containing some quasilinear operators with a matrix kernel where matrix entries satisfy discrete Oinarov condition. The research of weighted Hardy-type inequalities depends on the relations between parameters p, q and θ, so we considered the cases 1 < p ≤ q < θ < ∞ and p ≤ q < θ < ∞, 0 < p ≤1, criteria for the fulfillment of iterated discrete Hardy-type inequalities are obtained. Moreover, an alternative method of proof was shown in the work.

Keywords

• Inequality
• discrete Lebesgue space
• Hardy-type operator
• weight
• quasilinear operator
• matrix operator