NOTES ON THE BERGMAN PROJECTION TYPE OPERATOR IN C-n

In this paper, we will define the Bergman projection type operator P-r and find conditions on which the operator P-r is bound-ed on L-p (B, dv). By using the properties of the Bergman projection type operator P-r, we will show that if f epsilon L-a(p) (B, dv), then (1-vertical bar vertical bar w vertical bar vertical bar(2) ) del f (w) center dot z epsilon L-p (B, dv). We will also show that if (1-vertical bar vertical bar w vertical bar vertical bar(2)) del f(w) center dot z/(z,w) epsilon L-p (B,dv) then f epsilon L-a(p) (B,dv).