Let D be the open unit disk of the complex plane C and H(D) be the space of all analytic functions on D. Let A2γ,δ(D) be the space of analytic functions that are L2 with respect to the weight ωγ,δ(z)=(ln1|z|)γ[ln(1−1ln|z|)]δ, where −1<γ<∞ and δ≤0. For given g∈H(D), the integral-type operator Ig on H(D) is defined as
Igf(z)=∫z0f(ζ)g(ζ)dζ.
In this paper, we characterize the boundedness of Ig on A2γ,δ, whereas in the main result we estimate the essential norm of the operator. Some basic results on the space A2γ,δ(D) are also presented.
