On the note of C. L. Belna

Waterman, Daniel

doi:10.1090/S0002-9939-1980-0581001-7

On the note of C. L. Belna
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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.

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