A Montel Type Result for Subharmonic Functions

Supper, R.

Supper, R.

Bollettino dell'Unione Matematica Italiana, Tome 2 (2009), p. 423-444 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

This article is devoted to sequences $(u_{n})_{n}$ of subharmonic functions in $\mathbb{R}^{N}$ , with finite order, whose means $J_{u_{n}}(r)$ (over spheres centered at the origin, with radius r) satisfy such a condition as: $\forall r>0$ , $\exists A_{r}>0$ such that $J_{u_{n}}(r)\leq A_{r}$ , $\forall n\in\mathbf{N}$ . The paper investigates under which conditions one may extract a pointwise or uniformly convergent subsequence.

Publié le : 2009-06-01

MR 2537279 | Zbl 1178.31001

@article{BUMI_2009_9_2_2_423_0,
     author = {R. Supper},
     title = {A Montel Type Result for Subharmonic Functions},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {2},
     year = {2009},
     pages = {423-444},
     zbl = {1178.31001},
     mrnumber = {2537279},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2009_9_2_2_423_0}
}

Supper, R. A Montel Type Result for Subharmonic Functions. Bollettino dell'Unione Matematica Italiana, Tome 2 (2009) pp. 423-444. http://gdmltest.u-ga.fr/item/BUMI_2009_9_2_2_423_0/

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