Siberian Mathematical Journal

, Volume 44, Issue 4, pp 713–728 | Cite as

Criteria for (Sub-)Harmonicity and Continuation of (Sub-)Harmonic Functions

  • B. N. Khabibullin


We obtain criteria for harmonicity and subharmonicity of a function in a domain in R d , d≥2, in terms of special Arens–Singer and Jensen measures. We also establish a criterion for (sub-)harmonicity of a δ-subharmonic function in terms of the associated Riesz charge and special Arens–Singer and Jensen functions. To this end, we use the theorem of this article on continuation of (sub-)harmonic functions to polar sets.

harmonic function subharmonic function Jensen measure Arens–Singer measure 


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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • B. N. Khabibullin
    • 1
  1. 1.Bashkir State UniversityUfa

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