Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfy certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.
Lucia, Marcello and Puls, Michael J., "The p -Royden and p -Harmonic Boundaries for Metric Measure Spaces" (2015). CUNY Academic Works.