Conditional Carleson measures and related operators on Bergman spaces

In this paper first we define generalized Carleson mea- sure. Then we consider a special case of it, named conditional Carleson measure on the Bergman spaces. After that we give a characterization of conditional Carleson measures on Bergman spaces. Moreover, by using this characterization we find an equiv- alent condition to boundedness of weighted conditional expectation operators on Bergman spaces.