A family of integral inequalities on the circle S 1

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Abdellatif Bentaleb¹  Said Fahlaoui² 

[1] This paper was written while the rst author was visiting the International Centre for Theoretical Physics;University Moulay Ismail, Faculty of Sciences, Department of Mathematics and Informatics

关键词: Chebychev semigroup;    spectral gap;    Poincare inequality;    Sobolev inequality;    logarithmic Sobolev inequality.;   

DOI  :  10.3792/pjaa.86.55

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

We consider the Chebychev semigroup defined on the interval $\left [-1,+1\right ]$ by its Dirichlet form ${\int _{-1}^{+1}}(1-x^2)f^{\prime 2}(x)\, {\frac {dx}{ \pi \sqrt {1-x^2}}}$. We prove, via a method involving probabilistic techniques, a family of inequalities which interpolate between the Sobolev and Poincaré inequalities.

【 授权许可】

Unknown