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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Growth problems for subharmonic functions of finite order in space


Authors: N. V. Rao and Daniel F. Shea
Journal: Trans. Amer. Math. Soc. 230 (1977), 347-370
MSC: Primary 31B05; Secondary 30A70
MathSciNet review: 0444974
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Abstract: For a function $ u(x)$ subharmonic (or $ {C^2}$) in $ {{\mathbf{R}}^m}$, we compare the ``harmonics'' (defined in §1) of u with those of a related subharmonic function whose total Riesz mass in $ \vert x\vert \leqslant r$ is the same as that of u, but whose $ {L^2}$ norm on $ \vert x\vert = r$ is maximal, for all $ 0 < r < \infty $. We deduce estimates on the growth of the Riesz mass of u in $ \vert x\vert \leqslant r$, as $ r \to \infty $.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0444974-3
PII: S 0002-9947(1977)0444974-3
Article copyright: © Copyright 1977 American Mathematical Society