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

Abstract

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.

Keywords

• dirichlet problem at infinity
• metric measure space
• p-harmonic function
• p-parabolic
• p-royden algebra
• p-weak upper gradient
• (p, p)-sobolev inequality
• primary: 31b20; secondary: 31c25, 54e45