Hausdorff operators on some classical spaces of analytic functions

In this note, we start on the study of the sufficient conditions for the boundedness of Hausdorff operators align*(HK,μf)(z):=∫DK(w)f(σw(z))dμ(w)align* on three important function spaces (i.e., derivative Hardy spaces, weighted Dirichlet spaces, and Bloch type spaces), which is a continuation of the previous works of Mirotin et al. Here, μ is a positive Radon measure, K is a μ -measurable function on the open unit disk D , and σ w(z) is the classical Möbius transform of D .