Banach Journal of Mathematical Analysis

Norm estimates for random polynomials on the scale of Orlicz spaces

Andreas Defant and Mieczysław Mastyło

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We prove an upper bound for the supremum norm of homogeneous Bernoulli polynomials on the unit ball of finite-dimensional complex Banach spaces. This result is inspired by the famous Kahane–Salem–Zygmund inequality and its recent extensions; in contrast to the known results, our estimates are on the scale of Orlicz spaces instead of p-spaces. Applications are given to multidimensional Bohr radii for holomorphic functions in several complex variables, and to the study of unconditionality of spaces of homogenous polynomials in Banach spaces.

Article information

Banach J. Math. Anal., Volume 11, Number 2 (2017), 335-347.

Received: 2 February 2016
Accepted: 30 May 2016
First available in Project Euclid: 28 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

homogeneous polynomials interpolation spaces Orlicz spaces


Defant, Andreas; Mastyło, Mieczysław. Norm estimates for random polynomials on the scale of Orlicz spaces. Banach J. Math. Anal. 11 (2017), no. 2, 335--347. doi:10.1215/17358787-0000006X.

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