Let G be a locally compact second countable Hausdorff space with a positive regular Borel measure and ω is a weight on G. In this article, we provide necessary and sufficient conditions for the hypercyclic weighted translations acting on the weighted space $L^p(G,\omega )(1\le p<\mathrm{\infty })$ in two different cases. Also, some examples are given to illustrate that the results in the first case generalize the characterizations on hypercyclicity for unilateral weighted shifts studied by Salas [16], and the results in the second case generalize Chen and Chu's work in [8]. Furthermore, we give characterizations of hypercyclicity for adjoint operators of these weighted translations.

令G是具有正正则 Borel 测度的局部紧第二可数 Hausdorff 空间，ω 是G上的权重。在本文中，我们提供了作用于加权空间的超循环加权平移的充分必要条件${升}^{磷}(G,\omega )(1\le 磷<\mathrm{\infty })$在两种不同的情况下。此外，还给出了一些例子来说明第一种情况的结果概括了 Salas [16] 研究的单边加权移位的超循环特征，而第二种情况的结果概括了 Chen 和 Chu 在 [8] 中的工作。此外，我们给出了这些加权翻译的伴随算子的超循环特征。