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Proceedings of the American Mathematical Society

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On measures associated to superharmonic functions


Author: Ü. Kuran
Journal: Proc. Amer. Math. Soc. 36 (1972), 179-186
MSC: Primary 31B05
DOI: https://doi.org/10.1090/S0002-9939-1972-0316728-0
MathSciNet review: 0316728
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Abstract: Let u be a superharmonic function in an open set $ \Omega $ in $ {R^n}$ and let $ \mu $ be the positive Radon measure associated to u, i.e. $ \mu $ is a negative constant multiple of the distributional Laplacian $ \Delta u$ of u. Using mostly elementary techniques, the paper deals with the properties of $ \mu $ in the large, when $ u > 0$ and $ \Omega = {R^n}$, and in the small, in some neighbourhood of a point in $ \Omega $.


References [Enhancements On Off] (What's this?)

  • [1] A. F. Beardon, Integral means of subharmonic functions, Proc. Cambridge Philos. Soc. 69 (1971), 151–152. MR 0281937
  • [2] M. Brelot, Éléments de la théorie classique du potentiel, Les Cours de Sorbonne. 3e cycle, Centre de Documentation Universitaire, Paris, 1959 (French). MR 0106366
  • [3] Nicolaas du Plessis, An introduction to potential theory, Hafner Publishing Co., Darien, Conn.; Oliver and Boyd, Edinburgh, 1970. University Mathematical Monographs, No. 7. MR 0435422

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0316728-0
Keywords: Superharmonic functions in higher dimensions, superharmonic functions in two-dimensions, associated measures, integral representations
Article copyright: © Copyright 1972 American Mathematical Society

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