Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Removable singularities for $ H\sp{p}$-functions

Author: Pentti Järvi
Journal: Proc. Amer. Math. Soc. 86 (1982), 596-598
MSC: Primary 32A35; Secondary 31C10
MathSciNet review: 674087
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Given a domain $ D$ in $ {{\mathbf{C}}^n}$, a holomorphic function $ f$ on $ D$ is said to belong to $ {H^p}(D)$, $ 0 < p < \infty $, provided that $ \vert f \vert^p$ admits a harmonic majorant in $ D$. In this note it is shown that $ {H^p}(D\backslash E) = {H^p}(D)$ whenever $ E$ is a relatively closed polar subset of $ D$.

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

  • [1] Joseph A. Cima and Ian R. Graham, On the extension of holomorphic functions with growth conditions across analytic subvarieties, Michigan Math. J. 28 (1981), no. 2, 241–256. MR 616273
  • [2] Maurice Heins, Hardy classes on Riemann surfaces, Lecture Notes in Mathematics, No. 98, Springer-Verlag, Berlin-New York, 1969. MR 0247069
  • [3] P. Lelong, Fonctions plurisousharmoniques et formes différentielles positives, Gordon & Breach, Paris-London-New York (Distributed by Dunod éditeur, Paris), 1968 (French). MR 0243112
  • [4] M. Parreau, Sur les moyennes des fonctions harmoniques et analytiques et la classification des surfaces de Riemann, Ann. Inst. Fourier Grenoble 3 (1951), 103–197 (1952) (French). MR 0050023
  • [5] Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
  • [6] E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Mathematical Notes, No. 11. MR 0473215
  • [7] Shinji Yamashita, On some families of analytic functions on Riemann surfaces, Nagoya Math. J. 31 (1968), 57–68. MR 0219720

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32A35, 31C10

Retrieve articles in all journals with MSC: 32A35, 31C10

Additional Information

Keywords: $ {H^p}$-function, polar set, quasi-bounded harmonic function
Article copyright: © Copyright 1982 American Mathematical Society