aequationes mathematicae

, Volume 61, Issue 1–2, pp 49–62 | Cite as

Carleman's inequality: history and new generalizations

  • J. Pečarić
  • K. B. Stolarsky


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.

Keywords.A — G inequality, Carleman's inequality, arithmetic mean, geometric mean, Hardy's inequality, recurrent inequalities, weighted inequality. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel, 2001

Authors and Affiliations

  • J. Pečarić
    • 1
  • K. B. Stolarsky
    • 2
  1. 1.Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, Zagreb, Croatia HR
  2. 2.Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, USA US

Personalised recommendations