Annals of Functional Analysis

Hadamard gap series in weighted-type spaces on the unit ball

Bingyang Hu and Songxiao Li

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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.

Article information

Source
Ann. Funct. Anal., Volume 8, Number 2 (2017), 259-269.

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1488358821

Digital Object Identifier
doi:10.1215/20088752-0000011X

Mathematical Reviews number (MathSciNet)
MR3619321

Zentralblatt MATH identifier
1361.32007

Subjects
Primary: 30H99: None of the above, but in this section 46B99: None of the above, but in this section

Keywords
weighted-type space Hadamard gaps homogeneous polynomial

Citation

Hu, Bingyang; Li, Songxiao. Hadamard gap series in weighted-type spaces on the unit ball. Ann. Funct. Anal. 8 (2017), no. 2, 259--269. doi:10.1215/20088752-0000011X. https://projecteuclid.org/euclid.afa/1488358821


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References

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