The non-existence of the Fejer‒Riesz type result for some weighted Bergman spaces in the unit disc

Piotr Jakóbczak


In this note, we consider the analogues of the classical Fejer‒Riesz inequality for some weighted
Hilbert spaces of analytic functions in the unit disc. We prove that for some class of such spaces,
the Fejer-Riesz inequality type results do not hold.

Słowa kluczowe: Fejer-Riesz inequality, Bergman spaces of analytic functions

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 u = f dans la boule et dans le polydisque de Cn, Ann. Inst. Fourier, Grenoble, 30, 1980, 121-154.

Duren P.L., Theory of Hp-spaces, Academic Press, New York 1970.

Jakóbczak P., Exceptional sets of rays for functions from the Bergman space in the unit disc, Atti Sem. Mat. Fis. Univ. Modena 52, 2004, 267-282.

Jakóbczak P., The behaviour of the rays of functions from the Bergman and Fock spaces, Rend. Circolo Mat. Palermo 57, 2008, 255-263.

Jakóbczak P., The Fejer-Riesz type results for some weighted Hilbert spaces of analytic functions in the unit disc, Opuscula Math., 31, nr 4, 2011, 605-614.

Janas J., On a theorem of Lebow and Mlak for several commuting operators, Studia Math., 76, 1983, 249-253.

Schneider G., Knirsch W., About entire functions with special L2-properties on one-dimensional subspaces of Cn, Rend. Circolo Matematico Palermo 54, 2005, 234-240.

Peetre J., Hankel kernels of higher weight for the ball, Nagoya Math. J., 130, 1993, 183-192.