Inequalities for the composition of Green’s operator and the potential operator

Abstract

We first establish the L p-norm inequalities for the composition of Green's operator and the potential operator. Then we develop the L ϕ-norm inequalities for the composition in the L ϕ-averaging domains. Finally, we display some examples for applications.

Norm Comparison Estimates for the Composite Operator

“…Particularly, it is an important part in differential forms to research norm inequalities for an operator or composite operator. norm has been studied very thoroughly [1][2][3], so we try to establish the Lipschitz norm and BMO norm inequalities for the composition of the Hardy-Littlewood maximal operator and potential operator. It is useful to explore the properties of the weighted norms; see [4][5][6][7].…”