Generalized integration operators from Bloch type spaces to weighted BMOA Spaces

Abstract

Abstract In this paper, we consider a generalized integration operator I g , φ ( n ) f ( z ) = ∫ 0 z f ( n ) ( φ ( ζ ) ) g ( ζ ) d ζ $$I_{g,\varphi }^{(n)} f(z) = \int\limits_0^z {f^{(n)} (\varphi (\zeta ))g(\zeta )d\zeta } $$ induced by holomorphic maps g and φ of the open unit disk 𝔻, where φ(𝔻) ⊂ 𝔻 and n is a positive integer. We characterize boundedness and compactness of I g , φ ( n ) $I_{g,\varphi }^{(n)} $ from Bloch type spaces to weighted BMOA spaces by using logarithmic Carleson measure characterization of the weighted BMOA spaces.