New estimates of essential norm of an integral-type operator between Bloch-type spaces on the unit ball

Let H(B) be the class of all holomorphic functions on the unit ball B in C-n. For g is an element of H(B) with g(0) = 0 and phi a holomorphic self-map of B, the integral-type operator P-phi(g), recently introduced by S. Stevic, is defined by P-phi(g)(f)(z) = integral(1)(0) f(phi(tz))g(tz) dt/t, z is an element of B. In this paper, we give a new characterization for the boundedness of integral-type operator P-phi(g) between Bloch-type spaces on the unit ball B. We also calculate the essential norm of the operator P-phi(g), which leads to a new condition for the compactness of the operator P-phi(g).