Stability of the Brascamp-Lieb constant and applications
نویسندگان
چکیده
منابع مشابه
Stability of the Brascamp–lieb Constant and Applications
We prove that the best constant in the general Brascamp–Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear variants of the Brascamp–Lieb inequality which have arisen recently in harmonic analysis.
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E. Mossel and J. Neeman recently provided a heat flow monotonicity proof of Borell’s noise stability theorem. In this note, we develop the argument to include in a common framework noise stability, Brascamp-Lieb inequalities (including hypercontractivity), and even a weak form of Slepian inequalities. The scheme applies furthermore to families of measures with are more log-concave than the Gaus...
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We prove global versions of certain known nonlinear Brascamp– Lieb inequalities under a natural homogeneity assumption. We also establish a conditional theorem allowing one to generally pass from local to global nonlinear Brascamp–Lieb estimates under such a homogeneity assumption.
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We find all optimisers for the Brascamp–Lieb inequality, thus completing the problem which was settled in special cases by Barthe; Carlen, Lieb and Loss; and Bennett, Carbery, Christ and Tao. Our approach to the solution is based on the heat flow methods introduced by the second and third sets of authors above. We present the heat flow method in the form which is most appropriate for our study ...
متن کاملA Brascamp-Lieb type covariance estimate
In this article, we derive a new covariance estimate. The estimate has a similar structure as the Brascamp-Lieb inequality and is optimal for ferromagnetic Gaussian measures. It can be naturally applied to deduce decay of correlations of lattice systems of continuous spins. We also discuss the relation of the new estimate with known estimates like a weighted estimate due to Helffer & Ledoux. Th...
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ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2018
ISSN: 1080-6377
DOI: 10.1353/ajm.2018.0013