Two Classes Of Integral Operators Over The Siegel Upper Half-space

Our main result gives necessary and sufficient conditions for the boundedness of two class of integral operators over the Siegel upper half-space.where?(z,w):= i/2(wn-zn)-<z',w'>.and ?(z):= ?(z,z)= Im zn-|z'|2.Similary results on the unit ball in Cn have been raised and widely used.Since Siegel upper half-space is biholomorphically equivalent to the unit ball B in Cn,we construct the counterparts of the integral operator in the unit ball.The computations here are more subtle,and the results over Siegel upper half-space are different from the corresponding ones in the unit ball.