Q_p And M_p Norm In The Unit Ball Of C～n

In this paper, we study the norm squares B_p for Q_p spaces and norm squares A_p for M_p spaces on the unit ball of Cⁿ. We prove that B_p(f) ≤ C_p,q¹B_q(f) for (n - 1)/n < q < p < n/(n - 1), and A_p(f) ≤ c_p,qA_q(f) for p > q > (n - l)/n, where c_p,q^' and c_p,g are constants depending on p and q only. This is a stronger version of the known nesting properties. The relations between Q_p norm, M_p norm and the Bloch norm are given also.