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

Marcello Lucia; Michael J. Puls — 2015

Analysis and Geometry in Metric Spaces

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.

Zero divisors and $L^{p} (G)$ , II.

Linnell, Peter A.; Puls, Michael J. — 2001

The New York Journal of Mathematics [electronic only]

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

Zero divisors and L p ( G ) , II.

Zero divisors and $L^{p} (G)$ , II.