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http://dx.doi.org/10.4134/BKMS.2016.53.2.561

ON ABSOLUTE VALUES OF 𝓠K FUNCTIONS  

Bao, Guanlong (Department of Mathematics, Shantou University)
Lou, Zengjian (Department of Mathematics, Shantou University)
Qian, Ruishen (School of Mathematics and Computation Science, Lingnan Normal University)
Wulan, Hasi (Department of Mathematics, Shantou University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.2, 2016 , pp. 561-568 More about this Journal
Abstract
In this paper, the effect of absolute values on the behavior of functions f in the spaces $\mathcal{Q}_K$ is investigated. It is clear that $g{\in}\mathcal{Q}_K({\partial}{\mathbb{D}}){\Rightarrow}{\mid}g{\mid}{\in}\mathcal{Q}_K({\partial}{\mathbb{D}})$, but the converse is not always true. For f in the Hardy space $H^2$, we give a condition involving the modulus of the function only, such that the condition together with ${\mid}f{\mid}{\in}\mathcal{Q}_K({\partial}{\mathbb{D}})$ is equivalent to $f{\in}\mathcal{Q}_K$. As an application, a new criterion for inner-outer factorisation of $\mathcal{Q}_K$ spaces is given. These results are also new for $Q_p$ spaces.
Keywords
$\mathcal{Q}_K$ spaces; absolute values; inner-outer factorisation;
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