CONVERGENCE OF FOURIER-SERIES ALMOST EVERYWHERE AND IN THE L-METRIC

The following theorems are proved.Theorem 1.There exists a constant such that for any function there is a measurable function for which, and is a partial sum of the conjugate Fourier series, and is the conjugate function to and there exists a measurable function such that, is Lebesgue measure), and both the Fourier series of and its conjugate series converge almost everywhere and in the metric of. Bibliography: 11 titles. © 1979 IOP Publishing Ltd.