Abstract
We investigate the problem of approximation of functions ƒ holomorphic in the unit disk by means A ρ, r (f) as ρ → 1−. In terms of the error of approximation by these means, a constructive characteristic of classes of holomorphic functions H r p Lipα is given. The problem of the saturation of A ρ, r (f) in the Hardy space H p is solved.
Similar content being viewed by others
References
G. Hardy and J. E. Littlewood, “Some properties of fractional integrals. II,” Math. Z., 34, 403–439 (1931).
P. Duren, Theory of H p Spaces, Academic Press, New York (1970).
V. T. Gavrilyuk and A. I. Stepanets, “Problems of saturation of linear methods,” Ukr. Mat. Zh., 43, No. 3, 291–308 (1991).
A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 1, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, (2002).
P. Butzer and J. R. Nessel, Fourier Analysis and Approximation, Birkhäuser, Basel (1971).
A. Zygmund, “Smooth functions,” Duke Math. J., 12, 47–76 (1945).
A. Zygmund, Trigonometric Series [Russian translation], Vol. 1, Mir, Moscow (1965).
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1253–1260, September, 2007.
Rights and permissions
About this article
Cite this article
Savchuk, V.V. Approximation of holomorphic functions by Taylor-Abel-Poisson means. Ukr Math J 59, 1397–1407 (2007). https://doi.org/10.1007/s11253-007-0094-0
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11253-007-0094-0