Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 13, Number 1 (2019), 217-233.
On Hardy-type inequalities for weighted means
Our aim in this article is to establish weighted Hardy-type inequalities in a broad family of means. In other words, for a fixed vector of weights and a weighted mean , we search for the smallest extended real number such that
The main results provide a complete answer in the case when is monotone and satisfies the weighted counterpart of the Kedlaya inequality. In particular, this is the case if is symmetric, concave, and the sequence is nonincreasing. In addition, we prove that if is a symmetric and monotone mean, then the biggest possible weighted Hardy constant is achieved if is the constant vector.
Banach J. Math. Anal., Volume 13, Number 1 (2019), 217-233.
Received: 3 June 2018
Accepted: 23 July 2018
First available in Project Euclid: 16 November 2018
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Páles, Zsolt; Pasteczka, Paweł. On Hardy-type inequalities for weighted means. Banach J. Math. Anal. 13 (2019), no. 1, 217--233. doi:10.1215/17358787-2018-0023. https://projecteuclid.org/euclid.bjma/1542358830