We prove that the Lorentz sequence space is, in a precise sense, optimal among all symmetric Banach sequence spaces satisfying a Bohnenblust–Hille-type inequality for -linear forms or -homogeneous polynomials on . Motivated by this result we develop methods for dealing with subtle Bohnenblust–Hille-type inequalities in the setting of Lorentz spaces. Based on an interpolation approach and the Blei–Fournier inequalities involving mixed-type spaces, we prove multilinear and polynomial Bohnenblust–Hille-type inequalities in Lorentz spaces with subpolynomial and subexponential constants. An application to the theory of Dirichlet series improves a deep result of Balasubramanian, Calado and Queffélec.
"Bohnenblust–Hille inequalities for Lorentz spaces via interpolation." Anal. PDE 9 (5) 1235 - 1258, 2016. https://doi.org/10.2140/apde.2016.9.1235