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

Authors

Marcello Lucia, CUNY College of Staten IslandFollow
Michael J. Puls, CUNY John Jay CollegeFollow

Document Type

Article

Publication Date

5-5-2015

Abstract

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.

Comments

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.