eng
Science and Education Publishing
Journal of Mathematical Sciences and Applications
2333-8792
2017-06-09
5
1
19
23
10.12691/jmsa-5-1-3
JMSA2017513
article
Family of Functional Inequalities for the Uniform Measure
Khalid Boutahir
1
Ali Hafidi
hafidiali28@gmail.com
2
Département de Mathématiques & Informatique, Université My Ismail, B. P. 11 201 Zitoune, Meknès, MAROC
Faculté des Sciences et Techniques, B.P.509, Boutalamine Errachidia, MAROC
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.
http://pubs.sciepub.com/jmsa/5/1/3/jmsa-5-1-3.pdf
heat semigroup
legendre operator
spectral gap
poincaré inequality
sobolev inequality
logarithmic sobolev inequality
φ-entropy inequality