Necessary and sufficient conditions for boundedness and for compactness of weighted composition operators from the weighted Bergman-Privalov-type space to a weighted type space or a little weighted-type space on the unit ball in the -dimensional complex vector space are given. The spaces and the composition operator mentioned above are defined in the following way. Let be the unit ball in , be the space of all holomorphic functions on , be the normalized Lebesgue measure on and , where and is a normalization constant, that is, . For each and , the weighted Bergman-Privalov-type space is defined in the following way:
The weighted-type space is defined as the space that consists of all such that , where is a positive continuous function (a weight) on . The little weighted-type space consists of all such that
For , the corresponding weighted composition operator is defined by
where is a holomorphic self-map of and is fixed.