Möbius invariant Qpspaces associated with the Green's function on the unit ball of Cn

Caiheng Ouyang, Weisheng Yang, Ruhan Zhao
1998 Pacific Journal of Mathematics  
In this paper, function spaces Q p (B) and Q p,0 (B), associated with the Green's function, are defined and studied for the unit ball B of C n . We prove that Q p (B) and Q p,0 (B) are Möbius invariant Banach spaces and that Q p (B) = Bloch(B), Q p,0 (B) = B 0 (B) (the little Bloch space) when 1 < p < n/(n − 1), Q 1 = BMOA(∂B) and Q 1,0 (B) = VMOA(∂B). This fact makes it possible for us to deal with BMOA and Bloch space in the same way. And we give necessary and sufficient conditions on
more » ... ess (and compactness) of the Hankel operator with antiholomorphic symbols relative to Q p (B) (and Q p,0 (B)). Moreover, other properties about the above spaces and |ϕ z (w)|, ϕ z (w) ∈ Aut(B), are obtained.
doi:10.2140/pjm.1998.182.69 fatcat:qzap7bho4jai5ixrrqlkt72ebi