Journal of Mathematical Sciences and Applications
ISSN (Print): 2333-8784 ISSN (Online): 2333-8792 Website: http://www.sciepub.com/journal/jmsa Editor-in-chief: Prof. (Dr.) Vishwa Nath Maurya, Cenap ozel
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Journal of Mathematical Sciences and Applications. 2017, 5(1), 19-23
DOI: 10.12691/jmsa-5-1-3
Open AccessArticle

Family of Functional Inequalities for the Uniform Measure

Khalid Boutahir1 and Ali Hafidi2,

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

Pub. Date: June 09, 2017

Cite this paper:
Khalid Boutahir and 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

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:
heat semigroup legendre operator spectral gap poincaré inequality sobolev inequality logarithmic sobolev inequality φ-entropy inequality

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