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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 1, 2015

The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces

  • Marcello Lucia and Michael J. Puls


Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies 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.


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Received: 2015-1-23
Accepted: 2015-5-5
Published Online: 2015-6-1

© 2015 M. Lucia and M. J. Puls

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

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