On the best Hardy constant for quasi-arithmetic means and homogeneous deviation means

Original · EN

The aim of this paper is to characterize the so-called Hardy means, i.e., those means Mₙ₌₁∞ R+ⁿ+ that satisfy the inequality ∑ₙ₌₁∞ M(x₁,,xₙ) ≤ C∑ₙ₌₁∞ xₙ for all positive sequences (xₙ) with some finite positive constant C. The smallest constant C satisfying this property is called the Hardy constant of the mean M. In this paper we determine the Hardy constant in the cases when the mean M is either a concave quasi-arithmetic or a concave and homogeneous deviation mean.