ABSTRACT
The study of composition operators started from the late 1960’s. Since it is a natural mathematical object, and because of its bounteous connections with other mathematical areas, more and more mathematicians from various areas are getting interested in the theory of composition operators. More recently, weighted composition operators appeared on the stage. As a combination of composition operators and pointwise 260multiplication operators, weighted composition operators arise naturally. For example, surjective isometries on Hardy spaces H p and Bergman spaces A p , 1 ≤ p < ∞, p ≠ 2, are given by weighted composition operators. See [13] and [19].
