On density of smooth functions in weighted fractional Sobolev spaces

Abstract

We prove that smooth C ∞ functions are dense in weighted fractional Sobolev spaces on an arbitrary open set, under some mild conditions on the weight. We also obtain a similar result in non-weighted spaces defined by some kernel similar to x → |x| −d−sp . One may consider the results to be a version of the Meyers-Serrin theorem.