On a reverse form of the Brascamp-Lieb inequality
نویسنده
چکیده
We prove a reverse form of the multidimensional Brascamp-Lieb inequality. Our method also gives a new way to derive the Brascamp-Lieb inequality and is rather convenient for the study of equality cases. Introduction We will work on the space R with its usual Euclidean structure. We will denote by 〈, 〉 the canonical scalar product. In [BL], H. J. Brascamp and E. H. Lieb showed that for m ≥ n, p1, . . . , pm > 1 and a1, . . . , am ∈ R, the norm of the multilinear operator Φ from Lp1(R)× · · · × Lpm(R) into R defined by Φ(f1, . . . , fm) = ∫
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