Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
145-155
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-12-15
Twórcy
autor
- Institute of Mathematicsi, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland
Bibliografia
- [1] J.-P. Ferrier, Spectral Theory and Complex Analysis, North-Holland, 1973.
- [2] J. Globevnik and E. L. Stout, Highly noncontinuable functions on convex domains, Bull. Sci. Math. 104 (1980), 417-434.
- [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] P. Jakóbczak, Highly nonintegrable functions in the unit ball, Israel J. Math. 97 (1997), 175-181.
- [5] J. Janas, On a theorem of Lebow and Mlak for several commuting operators, Studia Math. 76 (1983), 249-253.
- [6] S. G. Krantz, Function Theory of Several Complex Variables, Wiley, 1982.
- [7] I. Lieb, Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten I, Math. Ann. 190 (1970), 6-44.
- [8] J. Siciak, Highly noncontinuable functions on polynomially convex sets, Zeszyty Naukowe Uniw. Jagiell. 25 (1985), 95-107.
- [9] S. Trapani, Complex retractions and envelopes of holomorphy, Proc. Amer. Math. Soc. 104 (1988), 145-148.
- [10] P. Wojtaszczyk, On highly nonintegrable functions and homogeneous polynomials, Ann. Polon. Math. 65 (1997), 245-251.
- [11] A. Zeriahi, Ensembles pluripolaires exceptionnels pour la croissance partielle des fonctions holomorphes, Ann. Polon. Math. 50 (1989), 81-91.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv70z1p145bwm