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Bohnenblust–Hille
inequalities for Lorentz spaces via interpolation
Andreas Defant and Mieczysław Mastyło |
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Vol. 9 (2016), No. 5, 1235–1258
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Abstract |
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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. |
Keywords
Bohnenblust–Hille inequality, Dirichlet polynomials,
Dirichlet series, homogeneous polynomials, interpolation
spaces, Lorentz spaces
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Mathematical Subject Classification 2010
Primary: 46B70, 47A53
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Milestones
Received: 14 January 2016
Revised: 12 February 2016
Accepted: 30 March 2016
Published: 29 July 2016
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Authors |
| Andreas Defant | |
| Institut für Mathematik Carl von Ossietzky Universität Postfach 2503 D-26111 Oldenburg Germany |
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| Mieczysław Mastyło | |
| Faculty of Mathematics and Computer
Science Adam Mickiewicz University in Poznań Umultowska 87 61-614 Poznań Poland |
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