J Austral Math Soc Ser A 43 pp291--300, 1987.

Pointwise Convergence of Trigonometric Series

Chang-Pao Chen

Abstract

We establish two results in the pointwise convergence problem of a trigonometric series

å |n| < ¥  cneint with liml¯ 1 limn®¥   ëlnû å |k| = n  |Dmck| = 0

for some nonnegative integer m. These results not only generalize Hardy's theorem, the Jordan test theorem and Fatou's theorem, but also complement the results on pointwise convergence of those Fourier series associated with known L¹-convergence classes. A similar result is also established for the case that

limn®¥ n+(n/ln) å |k|=n  |Dmck| = 0,

where {l_n} satisfies certain conditions.

1980 AMS Subject Classification: 42A20, 42A32

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Authors

Chang-Pao Chen

Department of Mathematics, Stanford University, Stanford, California 94305, U.S.A.