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The best constants in the multiple Khintchine inequality. (English) Zbl 07116673
First, the authors show that the Khintchine inequality and the mixed \((\ell _{p/(p-1)}\),\(\ell _{2})\)-Littlewood inequality are equivalent, that is: one can be obtained from the other one. In this way the cotype constants \(C_{2,p}\) of \(\ell _{p}\)-spaces for \(1\leq p\leq 2\) are obtained. Among other results are estimates of the optimal constants in the multiple Khintchine inequality and the optimal constants of the multilinear mixed \((\ell _{p/(p-1)}\),\(\ell _{2})\)-Littlewood inequality.
MSC:
46B09 Probabilistic methods in Banach space theory
46G25 (Spaces of) multilinear mappings, polynomials
60B11 Probability theory on linear topological spaces
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