On the Closure of Smooth Compactly Supported Functions in Weighted Hölder Spaces

详细

The closure of the set of smooth compactly supported functions in a weighted Hölder space on ℝⁿ, n ≥ 1, with a weight controlling the behavior at the point at infinity is described. As an application, a solvability criterion for operator equations generated by de Rham differentials both in these spaces and on the closure of the set of smooth compactly supported functions in them for n ≥ 2 is obtained.