On the Note of C. L. Belna

Daniel Waterman
1980 Proceedings of the American Mathematical Society  
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.
doi:10.2307/2043736 fatcat:yonofmlr2rb5lktpqbzm7oigrq