Carleman’s inequality

Theorem ([1], pp. 24) For positive real numbers {an}n=1, Carleman’s inequalityMathworldPlanetmath states that


Although the constant e (the natural log base) is optimal, it is possible to refine Carleman’s inequality by decreasing the weight coefficients on the right hand side [2].


  • 1 L. Hörmander, The Analysis of Linear Partial Differential Operators I, (Distribution theory and Fourier Analysis), 2nd ed, Springer-Verlag, 1990.
  • 2 B.Q. Yuan, RefinementsPlanetmathPlanetmath of Carleman’s inequality, Journal of Inequalities in Pure and Applied Mathematics, Vol. 2, Issue 2, 2001, Article 21.
Title Carleman’s inequality
Canonical name CarlemansInequality
Date of creation 2013-03-22 13:43:17
Last modified on 2013-03-22 13:43:17
Owner Koro (127)
Last modified by Koro (127)
Numerical id 5
Author Koro (127)
Entry type Definition
Classification msc 26D15