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April 2017 Norm estimates for random polynomials on the scale of Orlicz spaces
Andreas Defant, Mieczysław Mastyło
Banach J. Math. Anal. 11(2): 335-347 (April 2017). DOI: 10.1215/17358787-0000006X


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.


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Andreas Defant. Mieczysław Mastyło. "Norm estimates for random polynomials on the scale of Orlicz spaces." Banach J. Math. Anal. 11 (2) 335 - 347, April 2017.


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

zbMATH: 06694357
MathSciNet: MR3603344
Digital Object Identifier: 10.1215/17358787-0000006X

Primary: 46B70
Secondary: 47A53

Keywords: homogeneous polynomials , interpolation spaces , Orlicz spaces

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 2 • April 2017
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