results on the regularity of operators on -spaces are often proved by means of interpolation operators applied to estimates at the endpoints. a classical example is that of the hibert transform on the real line, the -behavior of which can be deduced from a weak  type (1,1) estimate and the marcinkiewicz interpolation theorem. attempts to apply this idea to the bergman projection on certain domains such as the hartogs triangle  in  lead to some unexpected endpoint behavior. in particular, we show that for the hartogs triangle, at the left endpoint  of the interval of -boundedness, the bergman projection  on this domain is of restricted strong type  in the sense of stein-weiss, that is, for a characteristic function  of a measurable subset , we have

for a constant  independent of . this now determines the -behavior of the bergman projection via classical interpolation results. we discuss several generalizations of this result to other domains. this is ongoing joint work with zhenghui huo of duke kunshan university, china.