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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 4, 2003, pp. 939–957
DOI: 10.4171/ZAA/1181

Published online: 2003-12-31

Integral Estimates for the Laplace-Beltrami and Green's Operators Applied to Differential Forms on Manifolds

Shuseng Ding[1]

(1) Seattle University, United States

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.

Keywords: Differential forms, Sobolev embedding, Laplace-Beltrami operator, Green's operator

Ding Shuseng: Integral Estimates for the Laplace-Beltrami and Green's Operators Applied to Differential Forms on Manifolds. Z. Anal. Anwend. 22 (2003), 939-957. doi: 10.4171/ZAA/1181