In this paper we characterize the boundedness, compactness, and weak compactness of the integration operators

$$\begin{aligned} T_g (f)(z)=\int _{0}^{z} f(w)g'(w)\ dw \end{aligned}$$

acting on the average radial integrability spaces RM(p, q). For these purposes, we develop different tools such as a description of the bidual of RM(p, 0) and estimates of the norm of these spaces using the derivative of the functions, a family of results that we call Littlewood–Paley type inequalities.

中文翻译：

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解析函数的平均径向可积空间中的积分算子

在本文中，我们描述了积分算子的有界性，紧致性和弱紧致性

$$ \ begin {aligned} T_g（f）（z）= \ int _ {0} ^ {z} f（w）g'（w）\ dw \ end {aligned} $$

作用于平均径向可积空间RM（p，  q）。为此，我们开发了不同的工具，例如描述RM（p，0）的投标值，并使用函数的导数估计了这些空间的范数，这是一类称为Littlewood-Paley型不等式的结果。