Removable singularities for $H^{p}$-functions
HTML articles powered by AMS MathViewer
- by Pentti Järvi PDF
- Proc. Amer. Math. Soc. 86 (1982), 596-598 Request permission
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 $| f |^p$ 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
- 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
- Maurice Heins, Hardy classes on Riemann surfaces, Lecture Notes in Mathematics, No. 98, Springer-Verlag, Berlin-New York, 1969. MR 0247069, DOI 10.1007/BFb0080775
- P. Lelong, Fonctions plurisousharmoniques et formes différentielles positives, Gordon & Breach, Paris-London-New York; distributed by Dunod Éditeur, Paris, 1968 (French). MR 0243112
- 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 50023, DOI 10.5802/aif.37
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Mathematical Notes, No. 11, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0473215
- Shinji Yamashita, On some families of analytic functions on Riemann surfaces, Nagoya Math. J. 31 (1968), 57–68. MR 219720, DOI 10.1017/S0027763000012630
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 596-598
- MSC: Primary 32A35; Secondary 31C10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0674087-4
- MathSciNet review: 674087