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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), 137-193. MR 0447953 (56:6263)
  • [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 behaviour of holomorphic functions of several complex variables, Princeton Univ. Press, Princeton, N. J., 1972. MR 0473215 (57:12890)
  • [4] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, N. J.,1971. MR 0304972 (46:4102)

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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

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