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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Two theorems on boundary values of analytic functions


Author: S. R. Barker
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
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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 [Enhancements On Off] (What's this?)

  • [1] C. Fefferman and E. M. Stein, 𝐻^{𝑝} spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 0447953, https://doi.org/10.1007/BF02392215
  • [2] G. H. Hardy and J. E. Littlewood, Some properties of conjugate functions, J. Reine Angew. Math. 167 (1932), 405-423.
  • [3] E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Mathematical Notes, No. 11. MR 0473215
  • [4] Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971. Princeton Mathematical Series, No. 32. MR 0304972

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0499312-3
Keywords: Maximal function, plurisubharmonic function, almost everywhere convergence
Article copyright: © Copyright 1978 American Mathematical Society