Integrability and convergence of modified sum under some generalized coefficient class in L1-metric

Abstract

The class S_r', a generalization of the class S'  of Fourier coefficients is used to investigate the integrability and convergence of modified sum under L¹-metric. The criterion for L¹-Convergence of r^th derivative of modified sum h_n is also obtained under the same class of Fourier coefficients.