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Optimisers for the Brascamp-Lieb inequality. (English) Zbl 1159.26007

The Brascamp-Lieb inequality is a broad generalization of Hölder’ s or Young’s inequality dealing with integration of separable measures. It has the form \(\int_H \prod_i f_i^{p_i}(B_i x)dx \leq C \prod_i (\int_{H_i} f_i)^{p_i}\) where \(H,H_i\) are finite-dimensional Hilbert spaces, \(B_i\) are linear maps, \(p_i\) are nonnegative numbers, \(f_i\) are nonnegative functions and \(C\) is a constant. The author deals with the problem of characterizing the \(B_i\) and \(p_i\) such that the corresponding constant \(C\) is finite and attains its smallest value.

MSC:

26D15 Inequalities for sums, series and integrals
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