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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Iterated limits in $ N\sp{\ast} (U\sp{n})$


Author: Carl Stephen Davis
Journal: Trans. Amer. Math. Soc. 178 (1973), 139-146
MSC: Primary 32A99
DOI: https://doi.org/10.1090/S0002-9947-1973-0315155-5
MathSciNet review: 0315155
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Abstract: It is shown that if f is in $ {N^\ast}({U^n})$, then the iterated limits of f are almost everywhere independent of the order of iteration. In fact, the iterated limit and the radial limit are equal almost everywhere.


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

  • [1] A. P. Calderón and A. Zygmund, Note on the boundary values of functions of several complex variables, Contributions to Fourier Analysis, Annals of Mathematics Studies, no. 25, Princeton University Press, Princeton, N. J., 1950, pp. 145–165. MR 0035833
  • [2] Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
  • [3] Kôsaku Yosida, Functional analysis, Second edition. Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York Inc., New York, 1968. MR 0239384
  • [4] A. Zygmund, On the boundary values of functions of several complex variables. I, Fund. Math. 36 (1949), 207–235. MR 0035832
  • [5] -, Trigonometric series, 2nd ed. reprinted, Cambridge Univ. Press, New York, 1968. MR 38 #4882.

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DOI: https://doi.org/10.1090/S0002-9947-1973-0315155-5
Article copyright: © Copyright 1973 American Mathematical Society