## Orlicz norm inequalities for the composite operator and applications.(English)Zbl 1275.26023

Summary: 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 $$L^\phi(\mu)$$-averaging domains. Finally, we give some specific examples of Young functions and apply them to the norm inequality for the composite operator.

### MSC:

 26B10 Implicit function theorems, Jacobians, transformations with several variables 26D20 Other analytical inequalities 30C65 Quasiconformal mappings in $$\mathbb{R}^n$$, other generalizations 31B10 Integral representations, integral operators, integral equations methods in higher dimensions 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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### References:

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