Abstract
In this paper, a necessary and sufficient condition for the inclusion of the class ΛBV in the class H ωp is found.
References
C. Jordan, “Sur la series de Fourier,” C. R. Acad. Sci., 92, 228–230 (1881).
N. Wiener, “The quadratic variation of a function and its Fourier coefficients,” Mass. J. Math., 3, 72–94 (1924).
L. C. Young, “Sur une généralisation de la notion de variation de puissance p-iéme bornée au sens de N. Wiener, et sur la convergence des séries de Fourier,” C. R. Acad. Sci., 204, 470–472 (1937).
D. Waterman, “On convergence of Fourier series of functions of generalized bounded variation,” Stud. Math.,44, 107–117 (1972).
S. Perlman and D. Waterman, “Some remarks on functions of Λ-bounded variation,” Proc. Amer. Math. Soc.,74, 113–118 (1979).
S. Perlman, “Functions of generalized variation,” Fund. Math., 105, 199–211 (1980).
S. Wang, “Some properties of the functions of Λ-bounded variation,” Sci. Sinica. Ser. A, 25, 149–160 (1982).
D. Waterman, On Λ-bounded variation,” Stud. Math.,57, 33–45 (1976).
D. Waterman, “On the summability of Fourier series of functions of Λ-bounded variation,” Stud. Math.,55, 87–95 (1976).
D. Waterman, “Fourier series of functions of Λ-bounded variation,” Proc. Amer. Math. Soc.,74, 119–123 (1979).
Z. A. Chanturia, “Modulus of variation of functions and its applications in the theory of Fourier series,” Dokl. Akad. Nauk SSSR,214, 63–66 (1974).
M. Avdispahic, “On the classes ΛBV and V[(v(n)],” Proc. Amer. Math. Soc.,95, 230–235 (1985).
O. Kovacik, “On the embedding H ω ⊂ V p ,” Math. Slovaca, 43, 573–578 (1993).
A. S. Belov, “Relations between some classes of generalized variation,” Repts Enlarged Sess. Sem. I. Vekua Inst. Appl. Math.,3, 11–13 (1988).
Z. A. Chanturia, “On the uniform convergence of Fourier series,” Mat. Sb.,100, 534–554 (1976).
T. Akhobadze, “Relations between H ω, V[v(n)] and BΛ (p(n)↑ ∞, ϕ) classes of functions,” Bull. Georg. Acad. Sci.,164, No. 3, 433–435 (2001).
M. V. Medvedeva, “On the inclusion of classes H ω,” Mat. Zametki, 64, 713–719 (1998).
H. Kita and K. Yoneda, “A generalization of bounded variation,” Acta Math. Hung., 56, 229–238 (1990).
U. Goginava, “Relations between some classes of functions,” Sci. Math. J.,53, No. 2, 223–232 (2001).
U. Goginava, “Relations between ΛBV and BV (p(n)↑∞) classes of functions,” Acta Math. Hung.,101, No. 4, 245–254 (2003).
Yu. E. Kuprikov, “Moduli of continuity of functions from Waterman classes,” Moscow Univ. Math. Bull.,52, No. 5, 46–49 (1997).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1557–1562, November, 2005.
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Goginava, U. On the imbedding of the Waterman class in the class h ωp . Ukr Math J 57, 1818–1824 (2005). https://doi.org/10.1007/s11253-006-0031-7
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DOI: https://doi.org/10.1007/s11253-006-0031-7