Composition operators induced by monomial symbols and symbols with φ(D)⊂D - Hua, Shanshan (Nanyang Technological University, 2021)
We work on a general class of Weighted spaces H(β) of holomorphic functions in the unit disk D and properties of composition operators Cφ. The results include characterizations for compactness, compact difference, closed range, cyclicity and complex symmetry of composition operators Cφ induced by monomial symbols. Moreover, the boundedness for Cφ induced by general analytic self maps φ, where the closure of φ(D) is a subset of D, are also studied.