The p-Royden and p-Harmonic Boundaries for Metric Measure 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-Royd...
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De Gruyter
2015-06-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.1515/agms-2015-0008 |
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doaj-df56f395cc0b4596af54bcbf739b37732021-09-06T19:39:45ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742015-06-013110.1515/agms-2015-0008agms-2015-0008The p-Royden and p-Harmonic Boundaries for Metric Measure SpacesLucia Marcello0Puls Michael J.1Department of Mathematics, College of Staten Island-CUNY, 2800 Victory Boulevard, Staten Island, NY 10314, USADepartment of Mathematics, John Jay College-CUNY, 524 West 59th Street, New York, NY 10019, USALet 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.https://doi.org/10.1515/agms-2015-0008dirichlet problem at infinitymetric measure spacep-harmonic functionp-parabolicp-royden algebrap-weak upper gradient(p, p)-sobolev inequalityprimary: 31b20; secondary: 31c25, 54e45 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Lucia Marcello Puls Michael J. |
| spellingShingle |
Lucia Marcello Puls Michael J. The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces Analysis and Geometry in Metric Spaces 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 |
| author_facet |
Lucia Marcello Puls Michael J. |
| author_sort |
Lucia Marcello |
| title |
The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces |
| title_short |
The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces |
| title_full |
The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces |
| title_fullStr |
The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces |
| title_full_unstemmed |
The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces |
| title_sort |
p-royden and p-harmonic boundaries for metric measure spaces |
| publisher |
De Gruyter |
| series |
Analysis and Geometry in Metric Spaces |
| issn |
2299-3274 |
| publishDate |
2015-06-01 |
| description |
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. |
| topic |
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 |
| url |
https://doi.org/10.1515/agms-2015-0008 |
| work_keys_str_mv |
AT luciamarcello theproydenandpharmonicboundariesformetricmeasurespaces AT pulsmichaelj theproydenandpharmonicboundariesformetricmeasurespaces AT luciamarcello proydenandpharmonicboundariesformetricmeasurespaces AT pulsmichaelj proydenandpharmonicboundariesformetricmeasurespaces |
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1717770138345799680 |