In this paper, we introduce a class of Mobius-invariant Banach spaces Qk of analytic functions on the unit ball of Cnwhere K are non-decreasing and non-negative functions, and V, G and d\(z) denote the invariant gradient, Green's function and the invariant volume measure respectively. We develop a general theory of these spaces and prove that: (1). Qk is non-trivial if and only if(2). Let B denote the Bloch space on the unit ball. Qk (?) B and Qk = B, if(3). QK2 (?) Qk1 , if there exists a t0 > 0 such that K1(t) ≤K2(t), for 0 < t < t0. (4). QK,O (?) QK if K(Ct) ≤ C'K(t); QK,O (?) B0We also study the Bloch-type spaces Bα(α > 0), which are defined byHere, we give an equivalent definition of Bα for any α > 0, and show that...
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