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May 2017 Hadamard gap series in weighted-type spaces on the unit ball
Bingyang Hu, Songxiao Li
Ann. Funct. Anal. 8(2): 259-269 (May 2017). DOI: 10.1215/20088752-0000011X

Abstract

We give a sufficient and necessary condition for an analytic function f(z) on the unit ball B in Cn with Hadamard gaps, that is, for f(z)=k=1Pnk(z) where Pnk(z) is a homogeneous polynomial of degree nk and nk+1/nkc>1 for all kN, to belong to the weighted-type space Hμ and the corresponding little weighted-type space Hμ,0 under some condition posed on the weighted funtion μ. We also study the growth rate of those functions in Hμ.

Citation

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Bingyang Hu. Songxiao Li. "Hadamard gap series in weighted-type spaces on the unit ball." Ann. Funct. Anal. 8 (2) 259 - 269, May 2017. https://doi.org/10.1215/20088752-0000011X

Information

Received: 9 August 2016; Accepted: 16 September 2016; Published: May 2017
First available in Project Euclid: 1 March 2017

zbMATH: 1361.32007
MathSciNet: MR3619321
Digital Object Identifier: 10.1215/20088752-0000011X

Subjects:
Primary: 30H99, 46B99

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.8 • No. 2 • May 2017
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