Generalized composition operator from Bloch-type spaces to mixed-norm space on the unit ball

Abstract

Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spaces Bω and Bω,0 to mixed-norm space H(p,q,φ) on the unit ball B .