This is an announcement for the paper "Bohnenblust-Hille inequalities for Lorentz spaces via interpolation" by Andreas Defant and Mieczyslaw Mastylo.
Abstract: We prove that the Lorentz sequence space $\ell_{\frac{2m}{m+1},1}$ 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 $\mathbb{C}^n$. 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-Queff'{e}lec, we show an application to the theory of Dirichlet series.
Archive classification: math.FA
Mathematics Subject Classification: 46B70, 47A53
Submitted from: mastylo@amu.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1508.05554
or