On Hardy type inequalities for weighted quasideviation means

Páles, Zsolt and Pasteczka, Pawel (2020) On Hardy type inequalities for weighted quasideviation means. MATHEMATICAL INEQUALITIES & APPLICATIONS, 23 (3). pp. 971-990. ISSN 1331-4343

Preview

Text 1910.05988.pdf Download (290kB) | Preview

Abstract

Using recent results concerning the homogenization and the Hardy property of weighted means, we establish sharp Hardy constants for concave and monotone weighted quasideviation means and for a few particular subclasses of this broad family. More precisely, for a mean D like above and a sequence (lambda(n)) of positive weights such that lambda(n)/(lambda(1) +...+lambda(n)) is nondecreasing, we determine the smallest number H is an element of (1,+infinity] such thatSigma(infinity lambda)(n=1)nD((x(1), ..., x(n)), (lambda(1),...,lambda(n))) <= H center dot Sigma(infinity)(n=1)lambda(n)x(n) for all x is an element of l(1)(lambda).It turns out that H depends only on the limit of the sequence (lambda(n)/(lambda(1) +... +lambda(n))) and the behaviour of the mean D near zero.

Actions (login required)

Edit Item