Necessary and sufficient conditions for $L^{1}$ convergence of trigonometric series
Authors:
John W. Garrett and Časlav V. Stanojević
Journal:
Proc. Amer. Math. Soc. 60 (1976), 68-71
MSC:
Primary 42A20
DOI:
https://doi.org/10.1090/S0002-9939-1976-0425480-3
MathSciNet review:
0425480
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Abstract: It is shown that for the class of cosine series satisfying $a(n)\log n = o(1)$ and $\Delta a(n) \geqslant 0$ that integrability and ${L^1}$ convergence occur together. Relaxing the monotonicity to bounded variation we show that our previous result cannot be extended.
- John W. Garrett and Časlav V. Stanojević, On $L^{1}$ convergence of certain cosine sums, Bull. Amer. Math. Soc. 82 (1976), no. 1, 129–130. MR 394001, DOI https://doi.org/10.1090/S0002-9904-1976-13990-0
- S. A. Teljakovskiĭ, A certain sufficient condition of Sidon for the integrability of trigonometric series, Mat. Zametki 14 (1973), 317–328 (Russian). MR 328456
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Keywords:
<IMG WIDTH="28" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${L^1}$"> convergence of Fourier series,
Fejér sums
Article copyright:
© Copyright 1976
American Mathematical Society
