@article{jmsa2017513,
author={{Boutahir, Khalid and Hafidi, Ali},
title={Family of Functional Inequalities for the Uniform Measure},
journal={Journal of Mathematical Sciences and Applications},
volume={5},
number={1},
pages={19--23},
year={2017},
url={http://pubs.sciepub.com/jmsa/5/1/3},
issn={2333-8792},
abstract={We consider on the interval [-1,1] the heat semigroup <img src=image/abs1.png></img> generated by the Legendre operator<i> </i><img src=image/abs2.png></img><i> </i>acting on the Hilbert space <img src=image/abs3.png></img> with respect to the uniform measure<i> </i><img src=image/abs4.png></img><i> </i><i> </i>By means of a simple method involving some semigroup techniques, we describe a large family of optimal integral inequalities with the Poincar¨¦ and logarithmic Sobolev inequalities as particular cases.},
doi={10.12691/jmsa-5-1-3}
publisher={Science and Education Publishing}
}