Sharp generalizations of the multilinear Bohnenblust--Hille inequality

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We prove that the multilinear Bohnenblust--Hille is a particular case of a quite general family of optimal inequalities.

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Summation of coefficients of polynomials on $\ell_{p}$ spaces (2013, background): “mmingmultilinearmappings. Wehaverecentlylearnedthatsomeparticularcasesofsomeofourresults(moreprecisely Proposition 3.1 for q =2 and the case (ia) in Proposition 4.4) have been independently obtainedin[1]. 14 V.DIMANTANDP. SEVILLA-PERIS Acknowledgements. ThisworkwasintitatedinJune2012,whentheﬁrstauth”
Multiple summing maps: Coordinatewise summability, inclusion theorems and p-Sidon sets (2017, background): “1), we fix u ∈ [1, 2] such that 1r = 1 u + 1 p − 1.”
Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators (2013, background): “k=1 ( (Cq(Y )Ksk,2) m−k CY,k )θk A particular case of Kahane’s inequality is Khintchine’s inequality: if (εi) is a sequence of independent Rademacher variables, then, for any p ∈ [1, 2], there exists a constant AR,p such that, for any n ≥ 1 and any a1 .”