On the boundedness of generalized integration operators on Hardy spaces

We study the boundedness and compactness properties of the generalized integration operator Tg,a when it acts between distinct Hardy spaces in the unit disc of the complex plane. This operator has been introduced in Chalmoukis (Proc Am Math Soc 148(8):3325–3337, 2020) by the first author in connection to a theorem of Cohn about factorization of higher order derivatives of functions in Hardy spaces. We answer in the affirmative a conjecture stated in the same work, therefore giving a complete characterization of the class of symbols g for which the operator is bounded from the Hardy space Hp to Hq,0<∞.