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

摘要

For a unit disk D in the complex plane, by H(D) denote the class of all holomorphic functions on D. We estimate the essential norms of integral-type operators (C-phi,g(m) f)(z) = integral(z)(0) f((m))(phi(xi))g(xi)d xi from weighted bergman spaces A(a)(p) into zygmund-type spaces Z(mu), where f,g is an element of H(D) and phi 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 C-phi,g(m) :A(alpha)(p) -> Z(mu) on D.