Some properties for random power series $ (\mathcal{R}f)(z) = \sum\limits_{n = 0}^\infty a_n\epsilon_n z^n $ in $ Q_K $ spaces and $ Q_{K, 0} $ spaces were studied in this paper. It was proved that if the condition $ \sum\limits_{n = 1}^\infty n|a_n|^2 K(\frac{1}{n}) < \infty $ holds, then $ \mathcal{R}f\in Q_K $ a.s. Furthermore, this condition actually implied that $ \mathcal{R}f\in Q_{K, 0} $ a.s. As an application, the relationship between mean Lipschitz spaces and $ Q_K $ spaces was shown.
Citation: RuiLan ZhuGe, Xinxin Zhao, Yan Wu. Taylor coefficients condition and mean growth of random series in $ Q_K $ spaces[J]. AIMS Mathematics, 2026, 11(7): 21961-21972. doi: 10.3934/math.2026887
Some properties for random power series $ (\mathcal{R}f)(z) = \sum\limits_{n = 0}^\infty a_n\epsilon_n z^n $ in $ Q_K $ spaces and $ Q_{K, 0} $ spaces were studied in this paper. It was proved that if the condition $ \sum\limits_{n = 1}^\infty n|a_n|^2 K(\frac{1}{n}) < \infty $ holds, then $ \mathcal{R}f\in Q_K $ a.s. Furthermore, this condition actually implied that $ \mathcal{R}f\in Q_{K, 0} $ a.s. As an application, the relationship between mean Lipschitz spaces and $ Q_K $ spaces was shown.
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RuiLan ZhuGe, Xinxin Zhao, Yan Wu. Taylor coefficients condition and mean growth of random series in $ Q_K $ spaces[J]. AIMS Mathematics, 2026, 11(7): 21961-21972. doi: 10.3934/math.2026887
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