Abstract of a paper by Andreas Defant and Mieczyslaw Mastylo
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 http://arXiv.org/abs/1508.05554
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alspach@math.okstate.edu