Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 5 (2016), 1235-1258.

Bohnenblust–Hille inequalities for Lorentz spaces via interpolation

Andreas Defant and Mieczysław Mastyło

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Abstract

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.

Article information

Source
Anal. PDE, Volume 9, Number 5 (2016), 1235-1258.

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1513097072

Digital Object Identifier
doi:10.2140/apde.2016.9.1235

Mathematical Reviews number (MathSciNet)
MR3531371

Zentralblatt MATH identifier
1357.46037

Subjects
Primary: 46B70: Interpolation between normed linear spaces [See also 46M35] 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20]

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

Citation

Defant, Andreas; Mastyło, Mieczysław. Bohnenblust–Hille inequalities for Lorentz spaces via interpolation. Anal. PDE 9 (2016), no. 5, 1235--1258. doi:10.2140/apde.2016.9.1235. https://projecteuclid.org/euclid.apde/1513097072


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