Holomorphic functions of fast growth on submanifolds of the domain

Piotr Jakóbczak

Annales Polonici Mathematici, Tome 69 (1998), p. 145-155 / Harvested from The Polish Digital Mathematics Library

Résumé

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 < ∞, ${f |}_{Π \cap D}$ is not $L^{p}$ -integrable on Π ∩ D.

Publié le : 1998-01-01

Zbl 0932.32002

EUDML-ID : urn:eudml:doc:262548

@article{bwmeta1.element.bwnjournal-article-apmv70z1p145bwm,
     author = {Piotr Jak\'obczak},
     title = {Holomorphic functions of fast growth on submanifolds of the domain},
     journal = {Annales Polonici Mathematici},
     volume = {69},
     year = {1998},
     pages = {145-155},
     zbl = {0932.32002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p145bwm}
}

Piotr Jakóbczak. Holomorphic functions of fast growth on submanifolds of the domain. Annales Polonici Mathematici, Tome 69 (1998) pp. 145-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv70z1p145bwm/

Bibliographie

[000] [1] J.-P. Ferrier, Spectral Theory and Complex Analysis, North-Holland, 1973.

[001] [2] J. Globevnik and E. L. Stout, Highly noncontinuable functions on convex domains, Bull. Sci. Math. 104 (1980), 417-434. | Zbl 0482.32002

[002] [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.

[003] [4] P. Jakóbczak, Highly nonintegrable functions in the unit ball, Israel J. Math. 97 (1997), 175-181. | Zbl 0887.32004

[004] [5] J. Janas, On a theorem of Lebow and Mlak for several commuting operators, Studia Math. 76 (1983), 249-253. | Zbl 0535.47003

[005] [6] S. G. Krantz, Function Theory of Several Complex Variables, Wiley, 1982. | Zbl 0471.32008

[006] [7] I. Lieb, Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten I, Math. Ann. 190 (1970), 6-44. | Zbl 0199.42702

[007] [8] J. Siciak, Highly noncontinuable functions on polynomially convex sets, Zeszyty Naukowe Uniw. Jagiell. 25 (1985), 95-107. | Zbl 0585.32012

[008] [9] S. Trapani, Complex retractions and envelopes of holomorphy, Proc. Amer. Math. Soc. 104 (1988), 145-148. | Zbl 0664.32008

[009] [10] P. Wojtaszczyk, On highly nonintegrable functions and homogeneous polynomials, Ann. Polon. Math. 65 (1997), 245-251. | Zbl 0872.32001

[010] [11] A. Zeriahi, Ensembles pluripolaires exceptionnels pour la croissance partielle des fonctions holomorphes, Ann. Polon. Math. 50 (1989), 81-91. | Zbl 0688.32004