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

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.

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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

Information

Published: March 2010
First available in Project Euclid: 3 March 2010

zbMATH: 1204.47046
MathSciNet: MR2641798
Digital Object Identifier: 10.3792/pjaa.86.55

Subjects:
Primary: 42A99
Secondary: 46E35

Keywords: Chebychev semigroup , Logarithmic Sobolev inequality , Poincaré inequality , Sobolev inequality , spectral gap

Rights: Copyright © 2010 The Japan Academy

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Vol.86 • No. 3 • March 2010
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