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A.Bentaleb,S.Fahlaoui, a family integral inequalities on the circle S1, Proc. Jpn. Acad., Ser. A 2010; 86: 55-59.

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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.

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