In this paper we give necessary conditions and sufficient conditions for the boundedness of multidimensional Hausdorff operator on weighted Lebesgue spaces. In particular, weestablish necessary and sufficient conditions for the boundedness of special type multidimensional Hausdorff operator on weighted Lebesgue spaces for monotone radial weight functions.Also, we get similar results for important operators of harmonic analysis which are specialcases of the multidimensional Hausdorff operator. The results are illustrated by a number ofexamples.
Mathematics Subject Classification (2010): 28C99; 46E30; 47G10.