Orlicz norm inequalities for the composite operator and applications

Abstract

Abstract 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 Lφ(µ)-averaging domains. Finally, we give some specific examples of Young functions and apply them to the norm inequality for the composite operator. 2000 Mathematics Subject Classification: Primary 26B10; Secondary 30C65, 31B10, 46E35.

Keywords

• Orlicz norm
• the projection operator
• the homotopy operator
• <it>L^&#966;</it>(<it>&#181;</it>)-averaging domains