  In this paper, we first introduce some new Morrey type spaces containing
generalized Morrey space and weighted Morrey space as special cases. Then we
discuss the strong type and weak type estimates for a class of
Calder\'on--Zygmund type operators $T_\theta$ in these new Morrey type spaces.
Furthermore, the strong type estimate and endpoint estimate of commutators
$[b,T_{\theta}]$ formed by $b$ and $T_{\theta}$ are established. Also we study
related problems about two-weight, weak type inequalities for $T_{\theta}$ and
$[b,T_{\theta}]$ in the Morrey type spaces and give partial results.
