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Cesàro Transforms of Fourier Coefficients of -functions
Author(s):
Jie
Xiao
Journal:
Proc. Amer. Math. Soc.
125
(1997),
3613-3616.
MSC (1991):
Primary 26D15, 42A05, 42A16
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Abstract:
In this note, we show that Cesàro transforms of Fourier cosine or sine coefficients of any -function are Fourier cosine or sine coefficients of some -function.
References:
- 1.
- E. Alshynbaeva, Transformations of Fourier coefficients of certain classes of functions, Math. Notes 25 (1979), 332-335. MR 81e:42007
- 2.
- K. Anderson, On the transformation of Fourier coefficients of certain classses of functions, Pacific J. Math. 100 (1983), 243-248. MR 84j:76056
- 3.
- G.H. Hardy, Notes on some points in the integral caculus LXVI, Messenger Math. 58 (1928), 50-52.
- 4.
- C.T. Loo, Note on the properties of Fourier coefficients, Amer. J. Math. 71 (1949), 269-282. MR 10:603e
- 5.
- D.A. Stegenga, Bounded Toeplitz operators on
and applications on the duality between and the functions of bounded mean oscillation, Amer. J. Math. 98 (1976), 573-589. MR 54:8340 - 6.
- E.M. Stein, Harmonic Analysis, real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, New Jersey, 1993. MR 95c:42002
- 7.
- A. Zygmund, Trigonometric Series I, Cambridge Univ. Press, 1968. MR 38:4882
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Additional Information:
Jie
Xiao
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People's Republic of China
Email:
jxiao@sxx0.math.pku.edu.cn
DOI:
10.1090/S0002-9939-97-04040-9
PII:
S 0002-9939(97)04040-9
Keywords:
Ces\`{a}ro transforms,
Fourier coefficients
Received by editor(s):
December 11, 1995
Received by editor(s) in revised form:
July 9, 1996
Additional Notes:
The author is partially supported by the National Science Foundation of China
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1997,
American Mathematical Society
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