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Blei’s inequality and coordinatewise multiple summing operators. (English) Zbl 1286.26017
Summary: Two inequalities resembling the multilinear Hölder inequality for mixed-norm Lebesgue spaces are proved. When specialized to single-function inequalities they include a pair of inequalities due to Blei and a recent extension of Blei’s inequality. The first of these inequalities is applied to give explicit indices in a known result for coordinatewise multiple summing operators. The second is used to prove a complementary result to the known one, again with explicit indices. As an application of the complementary result, a sufficient condition is given for a composition of operators to be multiple summing.

26D15 Inequalities for sums, series and integrals
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47H60 Multilinear and polynomial operators
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