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This article is cited in 1 scientific paper (total in 1 paper)
On Blaschke Products with Finite Dirichlet-Type Integral
R. V. Dallakjan State Engineering University of Armenia
Abstract:
The class of functions with finite Dirichlet-type integral is defined as the set of holomorphic functions $f$ in the unit disk satisfying the following condition:
$$
\int_{0}^{2\pi}\int_{0}^{1} (1-r)^{\alpha}|f'(re^{i\theta})|^{p} r\,dr\,d\theta,\qquad \alpha>-1,\quad 0<p<+\infty.
$$
These classes are usually denoted by $D_{\alpha}^p$. In this paper, we prove the converse of Rudin's theorem and thus provide a necessary and sufficient condition for a Blaschke product to belong to the class $D_{0}^{1}$.
Keywords:
Blaschke product, Dirichlet-type integral, Hardy class, holomorphic function.
Received: 16.11.2012
Citation:
R. V. Dallakjan, “On Blaschke Products with Finite Dirichlet-Type Integral”, Mat. Zametki, 96:6 (2014), 880–884; Math. Notes, 96:6 (2014), 943–947
Linking options:
https://www.mathnet.ru/eng/mzm10199https://doi.org/10.4213/mzm10199 https://www.mathnet.ru/eng/mzm/v96/i6/p880
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Abstract page: | 288 | Full-text PDF : | 152 | References: | 52 | First page: | 30 |
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