Singular integrals of the compositions of Laplace-Beltrami and Green's operators

Abstract

Abstract We establish the Poincaré-type inequalities for the composition of the Laplace-Beltrami operator and the Green's operator applied to the solutions of the non-homogeneous A-harmonic equation in the John domain. We also obtain some estimates for the integrals of the composite operator with a singular density.

Keywords

• Poincaré-type inequalities
• differential forms
• <it>A</it>-harmonic equations
• the Laplace-Beltrami operator
• Green's operator