Suppose \(p\ge 1\), \(w=P[F]\) is a harmonic mapping of the unit disk \({\mathbb D}\) satisfying F is absolutely continuous and \({\dot{F}}\in L^p(0, 2\pi )\), where \({\dot{F}}(e^{it})=\frac{\mathrm {d}}{\mathrm {d}t}F(e^{it})\). In this paper, we obtain Bergman norm estimates of the partial derivatives for w, i.e., \(\Vert w_z\Vert _{L^p}\) and \(\Vert \overline{w_{{\bar{z}}}}\Vert _{L^p}\), where \(1\le p<2\). Furthermore, if w is a harmonic quasiregular mapping of \({\mathbb {D}}\), then we show that \(w_z\) and \(\overline{w_{{\bar{z}}}}\) are in the Hardy space \(H^p\), where \(1\le p\le \infty \). The corresponding Hardy norm estimates, \(\Vert w_z\Vert _{p}\) and \(\Vert \overline{w_{{\bar{z}}}}\Vert _{p}\), are also obtained.

假设\（p \ ge 1 \），\（w = P [F] \）是单位磁盘\（{\ mathbb D} \）的谐波映射，满足F绝对连续，并且\（{\ dot {F }} \ L ^ p（0，2 \ pi）\）中，其中\（{\ dot {F}}（e ^ {it}）= \ frac {\ mathrm {d}} {\ mathrm {d} t} F（e ^ {it}）\）。在本文中，我们获得w的偏导数的Bergman范数估计，即\（\ Vert w_z \ Vert _ {L ^ p} \）和\（\ Vert \ overline {w _ {{\ bar {z}} }} \ Vert _ {L ^ p} \），其中\（1 \ le p <2 \）。此外，如果w是\（{\ mathbb {D}} \）的调和拟正则映射，则我们证明\（w_z \）和\（\ overline {w _ {{\ bar {z}}}} \）在Hardy空间\（H ^ p \）中，其中\（1 \ le p \ le \ infty \）。相应的哈迪模估计，\（\ Vert的w_z \ Vert的_ {P} \）和\（\ Vert的\划线{W _ {{\酒吧{}}} Z} \ Vert的_ {P} \），还获得。