On the note of C. L. Belna
HTML articles powered by AMS MathViewer
- by Daniel Waterman PDF
- Proc. Amer. Math. Soc. 80 (1980), 445-447 Request permission
Abstract:
The space of functions of ordered harmonic bounded variation (OHBV) has been shown by Belna to contain the space of functions of harmonic bounded variation (HBV) properly. OHBV is a Banach space and HBV is a first category subset. The ordered harmonic variation has continuity properties quite different from those of the harmonic variation. The relationship of these classes to the everywhere convergence of Fourier series is discussed.References
- Albert Baernstein II and Daniel Waterman, Functions whose Fourier series converge uniformly for every change of variable, Indiana Univ. Math. J. 22 (1972/73), 569–576. MR 310523, DOI 10.1512/iumj.1972.22.22047
- C. L. Belna, On ordered harmonic bounded variation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 441–444. MR 581000, DOI 10.1090/S0002-9939-1980-0581000-5
- Casper Goffman, Everywhere convergence of Fourier series, Indiana Univ. Math. J. 20 (1970/71), 107–112. MR 270048, DOI 10.1512/iumj.1970.20.20010
- 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, A characterization of the class of functions whose Fourier series converge for every change of variable, J. London Math. Soc. (2) 10 (1975), 69–74. MR 370036, DOI 10.1112/jlms/s2-10.1.69
- 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
- Daniel Waterman, Fourier series of functions of $\Lambda$-bounded variation, Proc. Amer. Math. Soc. 74 (1979), no. 1, 119–123. MR 521884, DOI 10.1090/S0002-9939-1979-0521884-1
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 445-447
- MSC: Primary 26A45
- DOI: https://doi.org/10.1090/S0002-9939-1980-0581001-7
- MathSciNet review: 581001