Q_k Spaces And Bloch-type Spaces On The Unit Ball Of C～n

In this paper, we introduce a class of Mobius-invariant Banach spaces Q_k 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). Q_k is non-trivial if and only if(2). Let B denote the Bloch space on the unit ball. Q_k (?) B and Q_k = B, if(3). Q_K2 (?) Q_k1 , if there exists a t₀ > 0 such that K₁(t) ≤K₂(t), for 0 < t < t₀. (4). Q_K,O (?) Q_K if K(Ct) ≤ C'K(t); Q_K,O (?) B₀We also study the Bloch-type spaces B^α(α > 0), which are defined byHere, we give an equivalent definition of B^α for any α > 0, and show that...