Cesàro Transforms of Fourier Coefficients
of -functions
Author:
Jie Xiao
Journal:
Proc. Amer. Math. Soc. 125 (1997), 3613-3616
MSC (1991):
Primary 26D15, 42A05, 42A16
DOI:
https://doi.org/10.1090/S0002-9939-97-04040-9
MathSciNet review:
1415377
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Abstract | References | Similar Articles | Additional Information
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.
- 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
Email:
jxiao@sxx0.math.pku.edu.cn
DOI:
https://doi.org/10.1090/S0002-9939-97-04040-9
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
Article copyright:
© Copyright 1997
American Mathematical Society