Abstract
In this note we study the behaviour of holomorphic functions from the Bergman and Fock spaces on the rays of the unit disc U and the complex plane ℂ. We obtain conditions on the finiteness of weighted L 2-integrals of those functions along rays.
Similar content being viewed by others
References
Arazy, J., Fisher, S., Peetre J.: Hankel operators on weighted Bergman spaces, Amer. J. Math., 110 (1988), 989–1053
Charpentier, P.: Formules explicites pour les solutions minimales de l’équation \( \bar \partial \) u = f dans la boule et dans le polydisque de ℂn, Ann. Inst. Fourier (Grenoble), 30 (1980), 121–154
Duren, P.: Theory of Hp spaces, (Pure and Applied Mathematics, Vol. 38) New York-London: Academic Press 1970
Jakóbczak, P.: Exceptional sets of rays for functions from the Bergman space in the unit disc, Atti Sem. Mat. Fis. Univ. Modena Reggio Emilia, 52 (2004), 267–282
Janas, J.: On a theorem of Lebow and Mlak for several commuting operators, Studia Math., 76 (1983), 249–253
Peetre, P.: Hankel kernels of higher weight for the ball, Nagoya Math. J., 130 (1993), 183–192
Knirsch, W., Schneider, G.: About entire functions with special L 2-properties on one-dimensional subspaces of ℂn, Rend.Circ. Mat. Palermo, 54 (2005), 234–240
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jakóbczak, P. The behaviour on the rays of functions from the Bergman and Fock spaces. Rend. Circ. Mat. Palermo 57, 255–263 (2008). https://doi.org/10.1007/s12215-008-0018-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12215-008-0018-3