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Cesàro Transforms of Fourier Coefficients
of $L^{\infty }$-functions

Author: Jie Xiao
Journal: Proc. Amer. Math. Soc. 125 (1997), 3613-3616
MSC (1991): Primary 26D15, 42A05, 42A16
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 $L^{\infty }(0,\pi )$-function are Fourier cosine or sine coefficients of some $BMO(0,\pi )$-function.

References [Enhancements On Off] (What's this?)

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Additional Information

Jie Xiao

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