In this paper we consider inequalities of the form ∞ ∑ M(x 1,..., xn) ≤ C xn, ∞ ∑ n=1 n=1 where M is a mean. The main results of the paper offer sufficient conditions on M so that the above inequality holds with a finite constant C. The results obtained extend Hardy's and Carleman's classical inequalities together with their various generalisations in a new direction.
|Number of pages||8|
|Journal||Bulletin of the Australian Mathematical Society|
|Publication status||Published - Dec 1 2004|
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