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<p>Abstract</p> <p>In this article, we first prove Orlicz norm inequalities for the composition of the homotopy operator and the projection operator acting on solutions of the nonhomogeneous A-harmonic equation. Then we develop these estimates to <it>L^&#966;</it>(<it>&#181;</it>)-averaging domains. Finally, we give some specific examples of Young functions and apply them to the norm inequality for the composite operator.</p> <p>2000 Mathematics Subject Classification: Primary 26B10; Secondary 30C65, 31B10, 46E35.</p>