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2016 Bohnenblust–Hille inequalities for Lorentz spaces via interpolation
Andreas Defant, Mieczysław Mastyło
Anal. PDE 9(5): 1235-1258 (2016). DOI: 10.2140/apde.2016.9.1235


We prove that the Lorentz sequence space 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 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. An application to the theory of Dirichlet series improves a deep result of Balasubramanian, Calado and Queffélec.


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Andreas Defant. Mieczysław Mastyło. "Bohnenblust–Hille inequalities for Lorentz spaces via interpolation." Anal. PDE 9 (5) 1235 - 1258, 2016.


Received: 14 January 2016; Revised: 12 February 2016; Accepted: 30 March 2016; Published: 2016
First available in Project Euclid: 12 December 2017

zbMATH: 1357.46037
MathSciNet: MR3531371
Digital Object Identifier: 10.2140/apde.2016.9.1235

Primary: 46B70 , 47A53

Keywords: Bohnenblust–Hille inequality , Dirichlet polynomials , Dirichlet series , homogeneous polynomials , interpolation spaces , Lorentz spaces

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.9 • No. 5 • 2016
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