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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the note of C. L. Belna


Author: Daniel Waterman
Journal: Proc. Amer. Math. Soc. 80 (1980), 445-447
MSC: Primary 26A45
MathSciNet review: 581001
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0581001-7
PII: S 0002-9939(1980)0581001-7
Article copyright: © Copyright 1980 American Mathematical Society