Two theorems on boundary values of analytic functions
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- by S. R. Barker PDF
- Proc. Amer. Math. Soc. 68 (1978), 54-58 Request permission
Abstract:
We give a new admissible maximal inequality for analytic functions of several complex variables, and also show that an analytic function which is admissibly bounded at almost all boundary points of a domain D must have an admissible limit a.e. These results are then applied to the boundary behaviour of the Nevanlinna class of D.References
- C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215 G. H. Hardy and J. E. Littlewood, Some properties of conjugate functions, J. Reine Angew. Math. 167 (1932), 405-423.
- 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
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 54-58
- MSC: Primary 32F05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0499312-3
- MathSciNet review: 0499312