On a Discrete Version of the Hardy–Littlewood–Polya Inequality Involving Multiple Parameters in the Whole Plane

Abstract

In this paper, by introducing multiple parameters, we establish a discrete version of the Hardy–Littlewood–Polya inequality in the whole plane. For the obtained inequality, we give the equivalent statements of the best possible constant factor linked to the parameters and deal with the equivalent inequalities. Our main result provided a new generalization of Hardy–Littlewood–Polya inequality, and as a consequence, we show that some new inequalities of the Hardy–Littlewood–Polya type can be derived from the current results by taking the special values of parameters.

Keywords

• Hardy–Littlewood–Polya inequality
• multiple parameters
• equivalent inequalities
• best possible constant factor