We obtain A_r(M)-weighted boundedness for compositions of Green's operator and the Laplace-Beltrami operator applied to differential forms on manifolds. As applications, we also prove A_r(M)-weighted Sobolev-Poincare embedding theorems for Green's operator and norm comparison theorems for solutions of the A-harmonic equation on manifolds. These results can be used in developing the Lp theory of differential forms and the Hodge decomposition.
Cite this article
Shuseng Ding, Integral Estimates for the Laplace-Beltrami and Green's Operators Applied to Differential Forms on Manifolds. Z. Anal. Anwend. 22 (2003), no. 4, pp. 939–957DOI 10.4171/ZAA/1181