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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.


This article was originally published in Analysis and Geometry in Metric Spaces, available at DOI 10.1515/agms-2015-0008

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.

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