Abstract
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.
Citation
Abdellatif Bentaleb. Said Fahlaoui. "A family of integral inequalities on the circle S1." Proc. Japan Acad. Ser. A Math. Sci. 86 (3) 55 - 59, March 2010. https://doi.org/10.3792/pjaa.86.55
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