... complicated and we do not have an equivalent conditionfor the boundedness of uCϕ: H∞α→H(p,q,φ) at the moment. Using the argument in the proof of Theorem 5.1 and the family of test functions ... pp. 465–474, 2006.[6]D.D.ClahaneandS.Stevi´c, “Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball,” Journal of Inequalities and Applications, vol. 2006, ArticleID ... B,weget the following result. We omit the details of the proof.Theorem 5.2. Suppose that ϕ is an analytic self-map of the unit ball, u∈ H(B), 0 <α,p, q<∞ ,and is normal on [0,1).Thenthefollowingstatementsholdtrue.(a)...