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A Class Of L¹-Convergence, R. Bojan1c, C. V. Stanojevic
A Class Of L¹-Convergence, R. Bojan1c, C. V. Stanojevic
Mathematics and Statistics Faculty Research & Creative Works
It is proved that if the Fourier coefficients (an) of /E L!(0, ir) satisfy (*)L" kp\Aan\p = o(l), for some 1
< 2, then \\sn- f\\ = o(l), if and only if a" lg n * o(l). For cosine trigonometric series with coefficients of bounded variation and satisfying (*) it is proved that a necessary and sufficient condition for the series to be a Fourier series is (an) E 6, where G is the Garrett-Stanojevic [4] class. © 1982 American Mathematical Society.