Real Analysis Exchange

Glaeser's Inequality on an Interval

Adam Coffman and Yifei Pan

Full-text: Open access

Abstract

We use elementary methods to find pointwise bounds for the first derivative of a real valued function with a continuous, bounded second derivative on an interval.

Article information

Source
Real Anal. Exchange, Volume 36, Number 2 (2010), 483-490.

Dates
First available in Project Euclid: 11 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.rae/1321020516

Mathematical Reviews number (MathSciNet)
MR3016732

Zentralblatt MATH identifier
1259.26022

Subjects
Primary: 26D10: Inequalities involving derivatives and differential and integral operators

Keywords
Calculus pointwise inequality and so on

Citation

Coffman, Adam; Pan, Yifei. Glaeser's Inequality on an Interval. Real Anal. Exchange 36 (2010), no. 2, 483--490. https://projecteuclid.org/euclid.rae/1321020516


Export citation

References

  • I. Capuzzo Dolcetta and A. Vitolo, $\cc^{1,\alpha}$ and Glaeser type estimates, Rendiconti di Matematica, Serie VII, 29 (2009), 17–27.
  • C. Chui and P. Smith, A note on Landau's problem for bounded intervals, Amer. Math. Monthly (9), 82 (1975), 927–929.
  • G. Glaeser, Racine carrée d'une fonction différentiable, Ann. Inst. Fourier (Grenoble) (2), 13 (1963), 203–210.
  • Y. Y. Li and L. Nirenberg, Generalization of a well-known inequality, in Contributions to Nonlinear Analysis, 365–370, Progr. Nonlinear Differential Equations Appl. 66, Birkhäuser, Basel, 2006.
  • T. Nishitani and S. Spagnolo, An extension of Glaeser inequality and its applications, Osaka J. Math. (1), 41 (2004), 145–157.