@inbook{6a05e2f357c943f9be581856cd2522cd,
title = "A family of integral inequalities on the interval [-1,1]",
abstract = "We study the heat semigroup (Formula Presented) generated by the Gegenbauer operator(Formula Presented), on the interval (Formula Presented) the normalization constant and n is a strictly positive real number. By means of a simple method involving essentially a commutation property between the semigroup and derivation, we describe a large family of optimal integral inequalities with logarithmic Sobolev and Poincar{\'e} inequalities as particular cases.",
keywords = "Gegenbauer operator, Heat semigroup, Logarithmic Sobolev inequality, Poincar{\'e}{\textquoteright}s inequality, Sobolev{\textquoteright}s inequality, Spectral gap, φ-entropy inequality",
author = "Ali Hafidi and Ammi, \{Moulay Rchid Sidi\} and Praveen Agarwal",
note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature Singapore Pte Ltd.",
year = "2018",
doi = "10.1007/978-981-13-3013-1\_17",
language = "English",
series = "Trends in Mathematics",
publisher = "Springer International Publishing",
pages = "323--331",
booktitle = "Trends in Mathematics",
address = "Switzerland",
}