In the present paper, we obtain characterization results of double Hausdorff matrices and apply these results to obtain error estimation of the functioñ f (x, y), conjugate to a function f (x, y) (periodic with period 2π in both x and y) in generalized Hölder space by double Hausdorff means of its double conjugate Fourier series. Some important corollaries are also obtained from our main result.