Let $ \nu $ be a standard weight on the upper half-plane G, i.e $\nu : G\longrightarrow (0,\infty)$ is continuous and satisfies $\nu(\omega)=\nu(i Im\omega), \omega\in G, \nu(it)\geq\nu(is)$ if $t\geq s>0 $ and $ \lim_{t\reightarrow 0}\nu(it)=0 $. Put $\nu_{1}(\omega)=Im\omega\nu(\omega), \omega\in G $. We characterize boundedness and surjectivity of the differentiation operator $ D :H_{\upsilon}(G)\longrightarrow H_{\upsilon_{1}}(G)$. For example we show that $ D $ is bounded if and only if $\nu $ is at most of moderate growth. We also study composition operator on Hv (G ).
