In the past, we established a module structure theorem for Sobolev spaces on open manifolds with bounded curvature and positive injectivity radius . The assumption was essential in the proof. But, manifolds with have been excluded. An extension of our former results to the case seems to be hopeless. In this paper, we show that certain Sobolev embedding theorems and a (generalized) module structure theorem are valid in weighted spaces with the weight or .
Cite this article
Jürgen Eichhorn, Chunpeng Wang, Sobolev Theorems for Cusp Manifolds. Z. Anal. Anwend. 32 (2013), no. 4, pp. 389–409DOI 10.4171/ZAA/1491