Bull. Korean Math. Soc. 2016; 53(2): 561-568
Printed March 31, 2016
https://doi.org/10.4134/BKMS.2016.53.2.561
Copyright © The Korean Mathematical Society.
Guanlong Bao, Zengjian Lou, Ruishen Qian, and Hasi Wulan
Shantou University, Shantou University, Lingnan Normal University, Shantou University
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.
Keywords: $\qk$ spaces, absolute values, inner-outer factorisation
MSC numbers: Primary 30D50, 30H25, 46E15
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