Composition operators on Hardy spaces

Abstract

The topic is composition operators f⟼f∘φ, where The symbol is holomorphic. We shall give a(non-exhaustive) overview of -more or less recent- results when these operators are viewed on the classical Hardy spaces Hp. The story involves some classical tools of complex analysis, as Nevanlinna counting function and Carleson measures. We will illustrate this presentation with miscellaneous examples and questions. Concerning the most recent results, we shall pay attention to their possible membership to the class of absolutely summing operators.