On a Li-Stević Integral-Type Operators between Different Weighted Bloch-Type Spaces

First, we introduce some basic notation which is used in this paper. Throughout the entire paper, the unit disk in the finite complex plane C will be denoted by D. H D will denote the space of all analytic functions on D. Every analytic self-map φ of the unit disk D induces through composition a linear composition operator Cφ fromH D to itself. It is a well-known consequence of Littlewood’s subordination principle 1 that the formula Cφ f f ◦ φ defines a bounded linear operator on the classical Hardy and Bergman spaces. That is, Cφ : H → H and Cφ : A → A are bounded operators. A problem that has received much attention recently is to relate function theoretic properties of φ to operator theoretic properties of the restriction of Cφ to various Banach spaces of analytic functions. Some characterizations of the boundedness and compactness of the composition operator between various Banach spaces of analytic functions can be found in 2–6 . Recently, Yoneda in 7 gave some necessary and sufficient conditions for a composition operator Cφ to be bounded and compact on the logarithmic Bloch space defined as follows: