Holomorphic functions of fast growth on submanifolds of the domain

Piotr Jakóbczak

Annales Polonici Mathematici (1998)

  • Volume: 70, Issue: 1, page 145-155
  • ISSN: 0066-2216

Abstract

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We construct a function f holomorphic in a balanced domain D in ℂ N such that for every positive-dimensional subspace Π of ℂ N , and for every p with 1 ≤ p < ∞, f | Π ∩ D is not L p -integrable on Π ∩ D.

How to cite

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Piotr Jakóbczak. "Holomorphic functions of fast growth on submanifolds of the domain." Annales Polonici Mathematici 70.1 (1998): 145-155. <http://eudml.org/doc/262548>.

@article{PiotrJakóbczak1998,
abstract = {We construct a function f holomorphic in a balanced domain D in $ℂ^N$ such that for every positive-dimensional subspace Π of $ℂ^N$, and for every p with 1 ≤ p < ∞, $f|_\{Π ∩ D\}$ is not $L^p$-integrable on Π ∩ D.},
author = {Piotr Jakóbczak},
journal = {Annales Polonici Mathematici},
keywords = {balanced domains; growth of holomorphic function; pseudoconvex balanced domain; holomorphic functions; growth},
language = {eng},
number = {1},
pages = {145-155},
title = {Holomorphic functions of fast growth on submanifolds of the domain},
url = {http://eudml.org/doc/262548},
volume = {70},
year = {1998},
}

TY - JOUR
AU - Piotr Jakóbczak
TI - Holomorphic functions of fast growth on submanifolds of the domain
JO - Annales Polonici Mathematici
PY - 1998
VL - 70
IS - 1
SP - 145
EP - 155
AB - We construct a function f holomorphic in a balanced domain D in $ℂ^N$ such that for every positive-dimensional subspace Π of $ℂ^N$, and for every p with 1 ≤ p < ∞, $f|_{Π ∩ D}$ is not $L^p$-integrable on Π ∩ D.
LA - eng
KW - balanced domains; growth of holomorphic function; pseudoconvex balanced domain; holomorphic functions; growth
UR - http://eudml.org/doc/262548
ER -

References

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  1. [1] J.-P. Ferrier, Spectral Theory and Complex Analysis, North-Holland, 1973. 
  2. [2] J. Globevnik and E. L. Stout, Highly noncontinuable functions on convex domains, Bull. Sci. Math. 104 (1980), 417-434. Zbl0482.32002
  3. [3] G. M. Henkin, Integral representation of functions holomorphic in strictly pseudoconvex domains and applications to the ∂̅-problem, Math. USSR-Sb. 11 (1970), 273-281. 
  4. [4] P. Jakóbczak, Highly nonintegrable functions in the unit ball, Israel J. Math. 97 (1997), 175-181. Zbl0887.32004
  5. [5] J. Janas, On a theorem of Lebow and Mlak for several commuting operators, Studia Math. 76 (1983), 249-253. Zbl0535.47003
  6. [6] S. G. Krantz, Function Theory of Several Complex Variables, Wiley, 1982. Zbl0471.32008
  7. [7] I. Lieb, Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten I, Math. Ann. 190 (1970), 6-44. Zbl0199.42702
  8. [8] J. Siciak, Highly noncontinuable functions on polynomially convex sets, Zeszyty Naukowe Uniw. Jagiell. 25 (1985), 95-107. Zbl0585.32012
  9. [9] S. Trapani, Complex retractions and envelopes of holomorphy, Proc. Amer. Math. Soc. 104 (1988), 145-148. Zbl0664.32008
  10. [10] P. Wojtaszczyk, On highly nonintegrable functions and homogeneous polynomials, Ann. Polon. Math. 65 (1997), 245-251. Zbl0872.32001
  11. [11] A. Zeriahi, Ensembles pluripolaires exceptionnels pour la croissance partielle des fonctions holomorphes, Ann. Polon. Math. 50 (1989), 81-91. Zbl0688.32004

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