Dora Pokaz

On a new class of Hardy-type inequalities

In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy, Hardy-Hilbert, Hardy-Littlewood-Pólya, and Pólya-Knopp inequalities as well as of Godunova’s and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.MSC: 26D10, 26D15.

Some New Refined General Boas-Type Inequalities

We state and prove a new refined Boas-type inequality in a setting with a topological space and general 𝜎-finite and finite Borel measures. As a consequence of the result obtained, we derive a new class of Hardy- and Polya-Knopp-type inequalities related to balls in ℝ𝑛 and prove that constant factors involved in their right-hand sides are the best possible.