Article citationsMore >>

E. Nelson, The free Markov field. J. Funct. Anal. 1973; 12: 211-227.

has been cited by the following article:

Article

Family of Functional Inequalities for the Uniform Measure

1Département de Mathématiques & Informatique, Université My Ismail, B. P. 11 201 Zitoune, Meknès, MAROC

2Faculté des Sciences et Techniques, B.P.509, Boutalamine Errachidia, MAROC


Journal of Mathematical Sciences and Applications. 2017, Vol. 5 No. 1, 19-23
DOI: 10.12691/jmsa-5-1-3
Copyright © 2017 Science and Education Publishing

Cite this paper:
Khalid Boutahir, Ali Hafidi. Family of Functional Inequalities for the Uniform Measure. Journal of Mathematical Sciences and Applications. 2017; 5(1):19-23. doi: 10.12691/jmsa-5-1-3.

Correspondence to: Ali  Hafidi, Faculté des Sciences et Techniques, B.P.509, Boutalamine Errachidia, MAROC. Email: hafidiali28@gmail.com

Abstract

We consider on the interval [-1,1] the heat semigroup generated by the Legendre operator acting on the Hilbert space with respect to the uniform measure By means of a simple method involving some semigroup techniques, we describe a large family of optimal integral inequalities with the Poincaré and logarithmic Sobolev inequalities as particular cases.

Keywords