Fourier series of functions of -bounded variation
Author:
Daniel Waterman
Journal:
Proc. Amer. Math. Soc. 74 (1979), 119-123
MSC:
Primary 42A16; Secondary 42A20
DOI:
https://doi.org/10.1090/S0002-9939-1979-0521884-1
MathSciNet review:
521884
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that the Fourier coefficients of functions of -bounded variation,
, are
. This was known for
. The classes L and HBV are shown to be complementary, but L and
are not complementary if
is not contained in HBV. The partial sums of the Fourier series of a function of harmonic bounded variation are shown to be uniformly bounded and a theorem analogous to that of Dirichlet is shown for this class of functions without recourse to the Lebesgue test.
- [1] Daniel Waterman, On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107–117. MR 310525, https://doi.org/10.4064/sm-44-2-107-117
- [2]
-, On the summability of Fourier series of functions of
-bounded variation, Studia Math. 55 (1976), 87-95.
- [3] Daniel Waterman, On 𝐿-bounded variation, Studia Math. 57 (1976), no. 1, 33–45. MR 417355, https://doi.org/10.4064/sm-57-1-33-45
- [4] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1979-0521884-1
Article copyright:
© Copyright 1979
American Mathematical Society