ESSENTIAL NORMS OF INTEGRAL-TYPE OPERATORS FROM WEIGHTED BERGMAN SPACES INTO ZYGMUND-TYPE SPACES.

For a unit disk D in the complex plane, by H(ⅅ) denote the class of all holomorphic functions on 픸. We estimate the essential norms of integral-type operators (Cφmgf(z) = ∫0zf(m(φ(<f(ξ))g(ξ)dξ from weighted bergman spaces Aαp into zygmund-type spaces Zμ, where f,g∈ H(ⅅ) and φ is an analytic self-map of ⅅ. Moreover, we obtain a new characterization for the boundedness and its essential norm in terms of the n--th power of φ of Cφm,g : A αp → Zμ on ⅅ. [ABSTRACT FROM AUTHOR]