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On absolute values of ${\mathcal{Q}_K}$ functions
Guanlong Bao,Zengjian Lou,Ruishen Qian,Hasi Wulan 대한수학회 2016 대한수학회보 Vol.53 No.2
In this paper, the effect of absolute values on the behavior of functions $f$ in the spaces $\qk$ is investigated. It is clear that $g\in \qkt \Rightarrow |g|\in \qkt$, 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 $|f|\in \qkt$ is equivalent to $f\in \qk$. As an application, a new criterion for inner-outer factorisation of $\qk$ spaces is given. These results are also new for $\qp$ spaces.
ON ABSOLUTE VALUES OF <sub>K</sub> FUNCTIONS
Bao, Guanlong,Lou, Zengjian,Qian, Ruishen,Wulan, Hasi Korean Mathematical Society 2016 대한수학회보 Vol.53 No.2
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.