Bohnenblust-Hille inequalities for Lorentz spaces via interpolation

2015/08/23 by Andreas Defant, Defant, Andreas, Mieczysław Mastyło +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1508.05554

Abstract

We prove that the Lorentz sequence space ℓ_(2m)/(m+1),1 is, in a~precise sense, optimal among all symmetric Banach sequence spaces satisfying a Bohnenblust-Hille type inequality for m-linear forms or m-homogeneous polynomials on ℂⁿ. 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. Improving a remarkable result of Balasubramanian-Calado-Queffélec, we show an application to the theory of Dirichlet series.

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