Annals of Functional Analysis

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

Bingyang Hu and Songxiao Li

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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

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

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

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Zentralblatt MATH identifier

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

weighted-type space Hadamard gaps homogeneous polynomial


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.

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