An extension theorem for $H^{p}$ functions
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- by Joseph A. Cima
- Proc. Amer. Math. Soc. 42 (1974), 529-532
- DOI: https://doi.org/10.1090/S0002-9939-1974-0326003-8
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Abstract:
Let V be a pure $(n - 1)$-dimensional variety in the polydisc ${U^n}$ with the distance from V to the torus ${\text {II}^n}$ positive and assume f is analytic on $\Omega \equiv {U^n}\backslash V$ Further let $u(z)$ be the real part of a function g analytic on $\Omega$ and assume $|f(z){|^p} \leqq u(z)$ for $z \in \Omega$. Then f can be analytically extended to a function $\hat f$ in ${H^p}({U^n})$.References
- Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
- 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
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Walter Rudin, Analytic functions of class $H_p$, Trans. Amer. Math. Soc. 78 (1955), 46–66. MR 67993, DOI 10.1090/S0002-9947-1955-0067993-3
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 529-532
- MSC: Primary 32D20; Secondary 30A78
- DOI: https://doi.org/10.1090/S0002-9939-1974-0326003-8
- MathSciNet review: 0326003