Carleman's inequality: history and new generalizations
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We do not believe there has been hitherto a systematic survey of Carleman's inequality and its history. Moreover, after Redheffer's 1967 paper on recurrent inequalities showed how Carleman's inequality could be obtained from a more general yet quite elementary inequality, there has been the possibility of producing very simple proofs of even stronger weighted generalizations and analogues of Carleman's inequality. Our aim here is to provide both the survey and the simple proofs. In particular, we give a weighted "Lorentz" analogue of Carleman's inequality.
- Carleman's inequality: history and new generalizations
Volume 61, Issue 1-2 , pp 49-62
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- Birkhäuser Verlag
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- Keywords.A — G inequality, Carleman's inequality, arithmetic mean, geometric mean, Hardy's inequality, recurrent inequalities, weighted inequality.