We define Hardy spaces \({\mathcal {H}}^p\) for quasiregular mappings in the plane, and show that for a particular class of these mappings many of the classical properties that hold in the classical setting of analytic mappings still hold. This particular class of quasiregular mappings can be characterised in terms of composition operators when the symbol is quasiconformal. Relations between Carleson measures and Hardy spaces play an important role in the discussion. This program was initiated and developed for Hardy spaces of quasiconformal mappings by Astala and Koskela in 2011 in their paper \({\mathcal {H}}^p\)-theory for Quasiconformal Mappings (Pure Appl Math Q 7(1):19–50, 2011).

我们为平面中的准正则映射定义了Hardy空间\（{\ mathcal {H}} ^ p \），并表明对于这些映射的特定类，解析映射的经典设置中仍然具有许多经典属性。当符号为准保形时，可以根据合成算符来表征此类特定的准正则映射。Carleson测度与Hardy空间之间的关系在讨论中起着重要作用。该程序是由Astala和Koskela在2011年的论文\（{\ mathcal {H}} ^ p \）-拟形映射的理论（Pure Appl Math Q 7（1）：19 ）中针对拟形映射的Hardy空间发起和开发的。–50，2011）。