Abstract: The relations of inclusion are studied between families of Stieltjes integrals and Bloch type space,Besov space,Bergman space on Cn.The following results are obtained:(1)If 0≤q＜p+1-n then βqJp；（2）If p≥0,q＞p+1 then Jpβq；(3)If q＞p≥0 then JpΔq；(4)If p＞0 then ΔpJp；(5)If 0＜p＜n+1 and 0＜q＜(n+1)/p then JpLqa；(6)If n+1＜p＜∞ and max｛0，n+1-(pn)/(n+1)｝＜σ＜1 then L(n+1)/paJp+σ.

Key words: families of Stieltjes intergrals, Bloch type space, Besov space, Bergman space, inclusion