Weighted Composition Operators on H2 and Applications

Operators on function spaces acting by composition to the right with a fixed selfmap phi of some set are called composition operators of symbol phi. A weighted composition operator is an operator equal to a composition operator followed by a multiplication operator. We summarize the basic properties of bounded and compact weighted composition operators on the Hilbert Hardy space on the open unit disk and use them to study composition operators on Hardy-Smirnov spaces.