Volterra Composition Operators between Weighted Bergman-nevanlinna and Bloch-type Spaces

Let g and φ be holomorphic maps on D such that φ(D) ⊂ D. Define Volterra composition operators Jg,φ and Ig,φ induced by g and φ as Jg,φf(z) = Z z 0 (f ◦ φ) (ζ) (g ◦ φ)′ (ζ) dζ and Ig,φf(z) = Z z 0 (f ◦ φ)′ (ζ) (g ◦ φ) (ζ) dζ for z ∈ D and f ∈ H(D), the space of holomorphic functions on D. In this paper, we characterize boundedness and compactness of these operators acting between weighted Bergman-Nevanlinna spaces AβN and Bloch-type spaces. In fact, we prove that Jg,φ : AβN → B α ( or Bα 0 ) and Ig,φ : A β N → B α (or Bα 0 ) are compact if and only if they are bounded.