The topic of this talk is composition operators \(f\longmapsto f\circ\varphi \, \), where the symbol is an analytic function from the complex unit disk to itself. We shall focus on the classical Hardy spaces \(H^p\) and give a (non-exhaustive) overview of -more or less recent- results. The story involves some classical tools of complex analysis, as Nevanlinna counting function and Carleson measures. Concerning the most recent results, we shall pay attention to their possible membership to the class of absolutely summing operators.
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