Poincaré-Type Inequalities for the Composite Operator in L ? -Averaging Domains

الملخص EN

We first establish the local Poincaré inequality with L ? -averaging domains for the composition of the sharp maximal operator and potential operator, applied to the nonhomogenous A -harmonic equation.

Then, according to the definition of L ? -averaging domains and relative properties, we demonstrate the global Poincaré inequality with L ? -averaging domains.

Finally, we give some illustrations for these theorems.