Walsh-Fourier series with coefficients of generalized bounded variation

摘要

We extend in different ways the class of null sequences of real numbers that are of bounded variation and study the Walsh-Fourier series of integrable functions on the interval [(0, 1) with such coefficients. We prove almost everywhere convergence as well as convergence in the pseu dometric of Lr(0, 1) for 0 < r < 1.