Fine properties of Newtonian functions and the Sobolev capacity on metric measure spaces
Fine properties of Newtonian functions and the Sobolev capacity on metric measure spaces
Newtonian spaces generalize first-order Sobolev spaces to abstract metric measure spaces. In this paper, we study regularity of Newtonian functions based on quasi-Banach function lattices. Their (weak) quasi-continuity is established, assuming density of continuous functions. The corresponding Sobolev capacity is shown to be an outer capacity. Assuming sufficiently high integrability …