L1-convergence of fourier series

Abstract

For an integrable function fon T, we introduce a modified partial sum [formula omitted] and establish its L1-convergence property. The relation between the sum and L1-convergence classes is also established. As a corollary, a new L1-convergence class is obtained. It is shown that this class covers all known L1-convergence classes. © 1986, Australian Mathematical Society. All rights reserved.