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Mean Value Property and Harmonicity on Carnot-Carathéodory Groups

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cris.lastimport.scopus2024-02-12T20:47:32Z
dc.abstract.enWe study strongly harmonic functions in Carnot–Carathéodory groups defined via the mean value property with respect to the Lebesgue measure. For such functions we show their Sobolev regularity and smoothness. Moreover, we prove that strongly harmonic functions satisfy the sub-Laplace equation for the appropriate gauge norm and that the inclusion is sharp. We observe that appropriate spherical harmonic polynomials in ℍ1 are both strongly harmonic and satisfy the sub-Laplace equation. Our presentation is illustrated by examples.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorAdamowicz, Tomasz
dc.contributor.authorWarhurst, Benjamin
dc.date.accessioned2024-01-25T05:34:42Z
dc.date.available2024-01-25T05:34:42Z
dc.date.copyright2018-10-25
dc.date.issued2020
dc.description.accesstimeAT_PUBLICATION
dc.description.financePublikacja bezkosztowa
dc.description.versionFINAL_PUBLISHED
dc.description.volume52
dc.identifier.doi10.1007/S11118-018-9740-4
dc.identifier.issn0926-2601
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/111962
dc.identifier.weblinkhttps://link.springer.com/article/10.1007%2Fs11118-018-9740-4
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofPotential Analysis
dc.relation.pages497-525
dc.rightsOther
dc.sciencecloudnosend
dc.subject.enCarnot group Harmonic Heisenberg group Lie algebra Lie group Laplace Maximum principle Mean value property Strongly harmonic Subelliptic equation Sub-Riemannian Weakly harmonic
dc.titleMean Value Property and Harmonicity on Carnot-Carathéodory Groups
dc.typeJournalArticle
dspace.entity.typePublication