Sarason transform in Sobolev space

The classical Sarason transform in a canonical isomorphism of the model space $H^2/\theta H^2$ ($\theta$ is an inner function generated by the single point mass) onto the standard $L^2$ space. In the paper the image of the space of smooth functions $H^1_2=\{f\colon f'\in H^2\}$ under this transform is described in explicit terms. The pointwise estimates of the model operator in $H^1_2/\theta H^1_2$ are obtained. Bibliography: 5 titles.