If \(\varphi \) is an entire function, the superposition operator \(S_\varphi \) is defined in the space \({\mathcal {H}}{\mathcal {o}}{\mathcal {l}}({\mathbb {D}})\) of all analytic functions f in the unit disc \({\mathbb {D}}\), by \(S_{\varphi }(f)=\varphi \circ f\). We consider the mixed norm spaces of Hardy type \(H(p,q,\alpha )\) (\(0<p,q\le \infty \), \(\alpha >0\)). In this work we provide a complete characterization of those entire functions \(\varphi \) so that the superposition operator \(S_\varphi \) maps \(H(p,q,\alpha )\) into \(H(s,t,\beta )\) for any two triplets of admissible parameters \((p,q,\alpha )\) and \((s,t,\beta )\). We also prove that superposition operators mapping a mixed norm space into another are bounded and continuous.

如果\（\ varphi \）是整个函数，则在空间\（{\ mathcal {H}} {\ mathcal {o}} {\ mathcal {l}}中定义叠加运算符\（S_ \ varphi \）单位圆盘\（{\ mathbb {D}} \）中所有分析函数f的（{\ mathbb {D}}）\），通过\（S _ {\ varphi} [f）= \ varphi \ circ f \ ）。我们考虑Hardy类型\（H（p，q，\ alpha）\）（\（0 <p，q \ le \ infty \），\（\ alpha> 0 \））的混合范数空间。在这项工作中，我们提供了所有函数\（\ varphi \）的完整表征，因此叠加算符\（S_ \ varphi \）映射\（H（p，q，\ alpha）\）将任意两个三元组的允许参数\（（p，q，\ alpha）\）和\（（s，t，\ beta）\）放入\（H（s，t，\ beta）\）中。我们还证明了将混合范数空间映射到另一个范数空间的叠加算子是有界且连续的。