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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

IMPACT FACTOR 2018: 0.536

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

Marcello Lucia
  • Corresponding author
  • Department of Mathematics, College of Staten Island-CUNY, 2800 Victory Boulevard, Staten Island, NY 10314, USA
  • Other articles by this author:
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/ Michael J. Puls
  • Corresponding author
  • Department of Mathematics, John Jay College-CUNY, 524 West 59th Street, New York, NY 10019, USA
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-06-01 | DOI: https://doi.org/10.1515/agms-2015-0008


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

MSC: Primary: 31B20; Secondary: 31C25, 54E45


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About the article

Received: 2015-01-23

Accepted: 2015-05-05

Published Online: 2015-06-01

Citation Information: Analysis and Geometry in Metric Spaces, Volume 3, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2015-0008.

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© 2015 M. Lucia and M. J. Puls. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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