Abstract
Different function spaces have certain inclusion or equivalence relations. In this paper, the author introduces a class of Möbius-invariant Banach spaces QK,0 (p,q) of analytic function on the unit ball of Cn, where K:(0,∞)→[0,∞) are non-decreasing functions and 0P∞, p/2-n-1q∞, studies the inclusion relations between QK,0 (p,q) and a class of B0α spaces which was known before, and concludes that QK,0 (p,q) is a subspace of B0(q+n+1)/p, and the sufficient and necessary condition on kernel function K(r) such that QK,0 (p,q)= B0(q+n+1)/p.
Highlights
QK spaces were first given by Hasi Wulan and Matts Essen around 2000
The notion of the spaces QK on the unit ball was defined by Xu Wen in his paper [4]
Definition 1 Let K : (0, ∞) → [0, ∞) is a right-continuous, non-decreasing function, for 0 < p < ∞, p − n −1 < q < ∞, we say that a holomorphic function 2 f belongs to the space QK,0 ( p, q) if
Summary
QK spaces were first given by Hasi Wulan and Matts Essen around 2000. In recent years, QK type spaces have caused extensive research (cf. [1]-[11]). Different function spaces have certain inclusion or equivalence relations. The author introduces a class of Möbius-invariant Banach spaces
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