REGULATED FUNCTIONS WHOSE FOURIER-SERIES CONVERGE FOR EVERY CHANGE OFVARIABLE

For any continuous and 2 pi-periodic function f, the GW condition is k nown to be necessary and sufficient for the everywhere convergence of the Fourier series of f circle g for every homeomorphism g of [-pi, pi ] with itself. It is shown that we may replace the continuous function s in this result by those which have right and left limits at each poi nt. (C) 1997 Academic Press.