Hausdorff operators on some classical spaces of analytic functions

Abstract In this note, we start on the study of the sufficient conditions for the boundedness of Hausdorff operators align* (H₊, f) (z): =₃K (w) f (w (z) ) d (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, is a positive Radon measure, K is a -measurable function on the open unit disk D, and w (z) is the classical Möbius transform of D.