On the classes $\Lambda \textrm {BV}$ and $\textrm {V}[\nu ]$
HTML articles powered by AMS MathViewer
- by M. Avdispahić PDF
- Proc. Amer. Math. Soc. 95 (1985), 230-234 Request permission
Abstract:
We prove inclusion relations between Waterman’s and Chanturiya’s classes and point to some corollaries thereof. The situation which occurs in connection with Zygmund’s theorem for Waterman’s classes is clarified.References
- N. K. Bari, Trigonometricheskie ryady, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). With the editorial collaboration of P. L. Ul′janov. MR 0126115 S. V. Bochkarev, On a problem of Zygmund, Math. USSR-Izv. 7 (1973), 629-637. Z. A. Chanturiya, The modulus of variation of a function and its application in the theory of Fourier series, Soviet. Math. Dokl. 15 (1974), 67-71.
- Z. A. Čanturija, The absolute convergence of Fourier series, Mat. Zametki 18 (1975), no. 2, 185–192 (Russian). MR 394010 —, On uniform convergence of Fourier series, Math. USSR-Sb. 29 (1976), 475-495. —, "On the absolute convergence of classes $V[{n^\alpha }]$," in Fourier analysis and approximation theory, Colloq. Math. Soc. Janos Bolyai 19 (1978), 219-240.
- Z. A. Chanturia, On the absolute convergence of Fourier series of the classes $H^{\omega }\cap V[v]$, Pacific J. Math. 96 (1981), no. 1, 37–61. MR 634761, DOI 10.2140/pjm.1981.96.37
- Z. A. Čanturija, The modulus of variation of a function and continuity, Sakharth. SSR Mecn. Akad. Moambe 80 (1975), no. 2, 281–283 (Russian, with Georgian and English summaries). MR 0404549
- Elaine Cohen, On the Fourier coefficients and continuity of functions of class $\scr V^{\ast } _{\Phi }$, Rocky Mountain J. Math. 9 (1979), no. 2, 227–237. MR 519938, DOI 10.1216/RMJ-1979-9-2-227
- Casper Goffman and Daniel Waterman, Functions whose Fourier series converge for every change of variable, Proc. Amer. Math. Soc. 19 (1968), 80–86. MR 221193, DOI 10.1090/S0002-9939-1968-0221193-7
- Casper Goffman and Daniel Waterman, The localization principle for double Fourier series, Studia Math. 69 (1980/81), no. 1, 41–57. MR 604353, DOI 10.4064/sm-69-1-41-57
- S. Perlman, Functions of generalized variation, Fund. Math. 105 (1979/80), no. 3, 199–211. MR 580582, DOI 10.4064/fm-105-3-199-211
- S. Perlman and D. Waterman, Some remarks on functions of $\Lambda$-bounded variation, Proc. Amer. Math. Soc. 74 (1979), no. 1, 113–118. MR 521883, DOI 10.1090/S0002-9939-1979-0521883-X
- Michael Schramm and Daniel Waterman, On the magnitude of Fourier coefficients, Proc. Amer. Math. Soc. 85 (1982), no. 3, 407–410. MR 656113, DOI 10.1090/S0002-9939-1982-0656113-1
- Rafat N. Siddiqi, Absolute convergence of Fourier series of a function of Wiener’s class $V_{p}$, Portugal. Math. 38 (1979), no. 1-2, 141–148 (1982). MR 682363
- Si Lei Wang, Some properties of the functions of $\Lambda$-bounded variation, Sci. Sinica Ser. A 25 (1982), no. 2, 149–160. MR 669675
- Daniel Waterman, On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107–117. MR 310525, DOI 10.4064/sm-44-2-107-117
- Daniel Waterman, On $L$-bounded variation, Studia Math. 57 (1976), no. 1, 33–45. MR 417355, DOI 10.4064/sm-57-1-33-45 —, On the summability of Fourier series of functions of $\Lambda$-bounded variation, Studia Math. 55 (1976), 87-95. —, Fourier series of functions of $\Lambda$-bounded variation, Proc. Amer. Math. Soc. 74 (1979), 119-123.
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 230-234
- MSC: Primary 26A45; Secondary 42A28
- DOI: https://doi.org/10.1090/S0002-9939-1985-0801329-7
- MathSciNet review: 801329