Bulletin of the
Korean Mathematical Society
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ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

On absolute values of ${\mathcal{Q}_K}$ functions

Guanlong Bao, Zengjian Lou, Ruishen Qian, and Hasi Wulan

Shantou University, Shantou University, Lingnan Normal University, Shantou University

Abstract

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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