Abstract
We consider the behavior of the ϕ-strong means of Fourier–Laplace series for functions that belong to L p(S m), p > 1, on a set of points of full measure on an m-dimensional sphere S m.
Similar content being viewed by others
REFERENCES
S. B. Topuriya, Fourier-Laplace Series on a Sphere [in Russian], Tbilisi University, Tbilisi (1987).
V. V. Khocholava, "On strong summability of Fourier - Laplace series for functions of the class L p(S k), p > 1," Soobshch. Akad. Nauk Gruz. SSR, 97, No. 3, 573–576 (1980).
V. Totik, "On the strong approximation by the ( c, d )-means of Fourier series. I, II," Anal. Math., 6, Nos. 1, 2, 57–85, 165-184 (1980).
E. Kogbetliantz, "Recherches sur la summabilité des series ultrasphériques par la méthode des moyennes arithmetiques," J. Math. Pures Appl., 9, No. 3, 107–187 (1924).
A. Zygmund, Trigonometric Series [Russian translation], Vol. II, Mir, Moscow (1965).
V. Totik, "On the strong approximation of Fourier series," Acta Math. Acad. Sci. Hung., 35, 157–172 (1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lasuriya, R.A. Characterization of the Points of ϕ-Strong Summability of Fourier–Laplace Series for Functions of the Class L p(S m), p > 1. Ukrainian Mathematical Journal 55, 55–67 (2003). https://doi.org/10.1023/A:1025068518235
Issue Date:
DOI: https://doi.org/10.1023/A:1025068518235