Characterization of the generalized Hausdorff and quasi Hausdorff operators on weighted integrable spaces

We examine the Hausdorff and Quasi Hausdorff matrices which act as an operator on Hardy spaces by its action on Taylor coefficients of an analytic function. Using the integral representation of the series on the Hardy spaces, we find the conditions on the weight functions on R+, to determine the boundedness of the operator on weighted integrable spaces and its adjoint operator on the respective domain.