Abstract

We give a new construction of holomorphic function with given almost all boundary values on a bounded strictly pseudoconvex domain Ω with the boundary of class C2C^2. Next we use this construction to solve the Radon inversion problem and describe exceptional sets for square integrals of holomorphic functions along complex directions.

Author information

Contact details are reproduced from the original publication and may be historical.

Piotr Kot

Instytut Matematyki, Politechnika Krakowska, ul. Warszawska 24, 31-155 Kraków, Poland

pkot@pk.edu.pl

Keywords

  • Inner function
  • Radon inversion problem

Mathematics Subject Classification

32A05, 32A35

References

  1. A. B. Aleksandrov: The existence of inner functions in the ball, Math. USSR, Sb. 46(2) (1983) 143–159.https://doi.org/10.1070/SM1983v046n02ABEH002759Google Scholar
  2. J. E. Fornaess: Strictly pseudoconvex domains in convex domains, Amer. J. Math. 98 (1976) 529–569.https://doi.org/10.2307/2373900Google Scholar
  3. J. Globevnik: Holomorphic functions which are highly non-integrable at the boundary, Israel J. Math. 115 (2000) 195–203.https://doi.org/10.1007/BF02810586Google Scholar
  4. P. Jakóbczak: Description of exceptional sets in the circles for functions from the Bergman space, Czech. Math. J. 47 (1997) 633–649.https://doi.org/10.1023/A:1022866501339Google Scholar
  5. P. Jakóbczak: Highly non-integrable functions in the unit ball, Israel J. Math 97 (1997) 175–181.https://doi.org/10.1007/BF02774034Google Scholar
  6. P. Jakóbczak: Exceptional sets of slices for functions from the Bergman Space in the ball, Canad. Math. Bull. 44(2) (2001) 150–159.https://doi.org/10.4153/CMB-2001-019-7Google Scholar
  7. P. Kot: Description of simple exceptional sets in the unit ball, Czech. Math. J. 54 (2004) 55–63.https://doi.org/10.1023/B:CMAJ.0000027246.96443.28Google Scholar
  8. P. Kot: Exceptional sets in convex domains, J. Convex Analysis 12(2) (2005) 351–364.https://doi.org/10.68381/jca12024Google Scholar
  9. S. G. Krantz: Function Theory of Several Complex Variables, PWN, Warsaw (1991).Google Scholar
  10. E. Løw: A construction of inner functions on the unit ball in Cp, Invent. Math. 67 (1982) 223–229.https://doi.org/10.1007/BF01393815Google Scholar
  11. E. Løw: Inner functions and boundary values in H ∞ (Ω) and A(Ω) in smoothly bounded pseudoconvex somains, Math. Z. 185 (1984) 191–210.https://doi.org/10.1007/BF01181690Google Scholar

Suggested citation

P. Kot. “A Holomorphic Function with Given Almost All Boundary Values on a Domain with Holomorphic Support Function.” Journal of Convex Analysis 14 (2007), No. 4, 693–704. https://doi.org/10.68381/jca14041

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Published by Heldermann Verlag, 2007. Rights now held by Banach Press.