Iterated limits in $N^{\ast } (U^{n})$
HTML articles powered by AMS MathViewer
- by Carl Stephen Davis
- Trans. Amer. Math. Soc. 178 (1973), 139-146
- DOI: https://doi.org/10.1090/S0002-9947-1973-0315155-5
- PDF | Request permission
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
- 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
- Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York, Inc., New York, 1968. MR 0239384, DOI 10.1007/978-3-662-11791-0
- A. Zygmund, On the boundary values of functions of several complex variables. I, Fund. Math. 36 (1949), 207–235. MR 35832, DOI 10.4064/fm-36-1-207-235 —, Trigonometric series, 2nd ed. reprinted, Cambridge Univ. Press, New York, 1968. MR 38 #4882.
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- 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