aequationes mathematicae

, Volume 61, Issue 1, pp 49–62

Carleman's inequality: history and new generalizations

  • J. Pečarić
  • K. B. Stolarsky

DOI: 10.1007/s000100050160

Cite this article as:
Pečarić, J. & Stolarsky, K. Aequ. math. (2001) 61: 49. doi:10.1007/s000100050160

Summary.

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.

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