Interpolating sequences in the polydisc
HTML articles powered by AMS MathViewer
- by Bo Berndtsson, Sun-Yung A. Chang and Kai-Ching Lin PDF
- Trans. Amer. Math. Soc. 302 (1987), 161-169 Request permission
Abstract:
Let ${H^\infty }({D^n})$ denote the set of all bounded analytic functions defined on the polydisc ${D^n}$ of ${{\mathbf {C}}^n}$. In this note, we give a sufficient condition for sequences of points in ${D^n}$ to be interpolating sequences for ${H^\infty }({D^n})$. We also discuss some conditions for interpolation of general domains.References
-
E. Amar, Interpolation dans le polydisque de ${{\mathbf {C}}^n}$, Analyse Harmonique Orsay, 207, 1976.
- Bo Berndtsson, Interpolating sequences for $H^\infty$ in the ball, Nederl. Akad. Wetensch. Indag. Math. 47 (1985), no. 1, 1–10. MR 783001
- Lennart Carleson, An interpolation problem for bounded analytic functions, Amer. J. Math. 80 (1958), 921–930. MR 117349, DOI 10.2307/2372840
- Sun-Yung A. Chang, Carleson measure on the bi-disc, Ann. of Math. (2) 109 (1979), no. 3, 613–620. MR 534766, DOI 10.2307/1971229
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- Peter W. Jones, $L^{\infty }$ estimates for the $\bar \partial$ problem in a half-plane, Acta Math. 150 (1983), no. 1-2, 137–152. MR 697611, DOI 10.1007/BF02392970
- Eric P. Kronstadt, Interpolating sequences in polydisks, Trans. Amer. Math. Soc. 199 (1974), 369–398. MR 417451, DOI 10.1090/S0002-9947-1974-0417451-0
- Nicholas Th. Varopoulos, Sur un problème d’interpolation, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A1539–A1542 (French). MR 303279
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 302 (1987), 161-169
- MSC: Primary 32A35; Secondary 30E05
- DOI: https://doi.org/10.1090/S0002-9947-1987-0887503-9
- MathSciNet review: 887503