... transform. In this article, we prove theconverse of the main theorem of [5] by adding a doubling condition for a weight func-tion. And then by adding a suitable regularity condition on a weight ... anecessary and sufficient condition on two-weighted norm inequalities for the Poissonintegral operator. And then, Sawyer [18,19] obtained characterizations of tw o-weightednorm inequalities for the ... ET: Two weight norm inequalities for certain maximal and integral operators. In Harmonic Analysis(Minneapolis, MN, 1981), Lecture Notes in Mathematics, vol. 908,Springer, Berlin (1982)8. Garcia-Cuerva,...