Carleman's inequality for finite series

@inproceedings{Bruijn1963CarlemansIF,
  title={Carleman's inequality for finite series},
  author={N. D. Bruijn},
  year={1963}
}
• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version… Expand
An asymptotic method in the theory of series
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version ofExpand
Carleman's Inequality
TLDR
The arithmeticgeometric mean inequality (AGM) asserts that y, < An, with equality if and only if the sequence {an} is constant, which is perhaps surprising a priori that the AGM-inequality is so. Expand
Carleman's inequality : history, proofs and some new generalizations
Carleman's inequality reads where , are positive numbers. In this paper we present some simple proofs of and several remarks (e.g. historical) about the inequality and its corresponding continuous ...
Classical Hardy’s and Carleman’s Inequalities and Mixed Means
The aim of this paper is to present an alternative approach to the classical discrete and integral Hardy’s and Carleman’s inequalities, considering their natural connection with discrete and integralExpand
Hilbert and Hardy type inequalities
The Thesis gives far reaching generalisations of the work of Dragomir–Kim (2003), Pachpatte (1987, 1990, 1992), Handley–Koliha–Pecaric (2000), Hwang– Yang (1990), Hwang (1996), Love–Pecaric (1995)Expand
Finite Sections of Weighted Carleman's Inequality
We study finite sections of weighted Carleman's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant.
Mixed Means and Hardy's Inequality
Integral means of arbitrary order, with power weights, and their companion means are introduced and related mixed-means inequalities are derived. These results are then used in proving inequalitiesExpand
The power method for lp norms
Abstract An iterative method is described which rapidly computes the norm of a nonnegative matrix A, considered as a mapping from the finite dimensional space l r(n) to the space l p(m). In caseExpand
Hardy’s, Carleman’s and Related Inequalities
Some preliminaries. Theorem 1. If p > 1, a n ≥ 0, and A n = a 1 + a 2 +... + a n, then $${\sum\limits_1^\infty {\left( {\frac{{{A_n}}}{n}} \right)} ^p} < {\left( {\frac{p}{{p - 1}}}Expand

References

SHOWING 1-2 OF 2 REFERENCES
On Hilbert's inequality in $n$ dimensions
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version ofExpand