期刊论文详细信息
Proceedings of the Japan Academy, Series A. Mathematical Sciences | |
A family of integral inequalities on the circle S 1 | |
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
【 预 览 】
Files | Size | Format | View |
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RO202106300000553ZK.pdf | 136KB | download |