Cesàro transforms of Fourier coefficients of 𝐿^{{}∞}-functions

Xiao, Jie

doi:10.1090/S0002-9939-97-04040-9

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
DOI: https://doi.org/10.1090/S0002-9939-97-04040-9
MathSciNet review: 1415377
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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.

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