We have developed some convergence criteria for the weighted composition operators on various Banach spaces of holomorphic functions, which also extends some of the results of Chalendar and Partington (Weighted Composition Operators: Isometries and Asymptotic Behaviour, 2019). We have also characterized the isometries of the weighted composition operators on the Hardy spaces \(H^p({\mathbb {D}})\), which extends the characterization of the isometric weighted composition operators on the Hardy-Hilbert space \(H^2({\mathbb {D}})\) done in Kumar and Partington (Oper Theory Adv Appl 153:157–167).

我们为全纯函数的各个Banach空间上的加权合成算子开发了一些收敛准则，这也扩展了Chalendar和Partington的一些结果（加权合成算子：Isometries和渐近行为，2019年）。我们还对Hardy空间\（H ^ p（{\ mathbb {D}}）\）上加权合成算子的等距进行了刻画，从而扩展了Hardy-Hilbert空间\（ H ^ 2（{\ mathbb {D}}）\）在Kumar和Partington中完成（Oper Theory Adv Appl 153：157-167）。