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In this paper we continue the study of Bergman theory for the class of sliceregular functions.  In the slice regular setting there are two possibilities to introduce theBergman spaces, that are called of the first and of the second kind. In thispaper we mainly consider the Bergman theory of the second kind, by providing anexplicit description of the Bergman kernel in the case of the unit ball and ofthe half space. In the case of the unit ball, we study the Bergman-Scetransform. We also show that the two Bergman theories can be compared only ifsuitable weights are taken into account. Finally, we use the Schwarz reflectionprinciple to relate the Bergman kernel with its values on a complex half plane.

Further properties of the Bergman spaces of slice regular functions