Tauberian -convergence classes of Fourier series. I
Authors:
William O. Bray and Časlav V. Stanojević
Journal:
Trans. Amer. Math. Soc. 275 (1983), 59-69
MSC:
Primary 42A32; Secondary 42A20
DOI:
https://doi.org/10.1090/S0002-9947-1983-0678336-3
MathSciNet review:
678336
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Abstract | References | Similar Articles | Additional Information
Abstract: It is shown that the Stanojević [2] necessary and sufficient conditions for -convergence of Fourier series of
can be reduced to the classical form. A number of corollaries of a recent Tauberian theorem are obtained for the subclasses of the class of Fourier coefficients satisfying
for some
. For Fourier series with coefficients asymptotically even with respect to a sequence
, and satisfying
![$\displaystyle l_n^{ - 1/q}{\left({\sum\limits_{k = n}^{n + [n/{l_n}]} {{k^{p - ... ...} {\vert^p}} \right)^{1/p}} = o(1)\, \quad (n \to \infty), \quad 1/p + 1/q = 1,$](images/img9.gif)

![$ {l_n} = [\parallel {\sigma _n}(f) - f{\parallel ^{ - 1}}]$](images/img11.gif)


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-, Tauberian conditions for the
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1983-0678336-3
Keywords:
-convergence of Fourier series
Article copyright:
© Copyright 1983
American Mathematical Society