Abstract
It is well known that sets of p-capacity zero are removable for bounded p-harmonic functions, but on metric spaces there are examples of removable sets of positive capacity. In this paper, we show that this can happen even on unweighted Rn when n>p, although only in very special cases. A complete characterization of removable singularities for bounded A-harmonic functions on weighted Rn, n≥1, is also given, where the weight is p-admissible. The same characterization is also shown to hold for bounded quasiharmonic functions on weighted Rn, n≥2, as well as on unweighted R. For bounded A-superharmonic functions and bounded quasisuperharmonic functions on weighted Rn, n≥2, we show that relatively closed sets are removable if and only if they have zero capacity.
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