and bounded mean oscillation 
by 

Abstract: Hardy and Littlewood showed in 1928 that if f is in the mean Lipschitz space L(p, 1/p) and the Fourier series for f is Cesaro summable at a point, then the series converges at that point. The principal result in the present paper is a proof that the same conclusion holds under the weaker hypothesis of Abel summability. A simple direct proof is given of the fact that L(p, 1/p) lies in BMO, (first proved for p = 2, by Cima and Petersen). The paper concludes with a survey of a few places in which these spaces arise naturally. 
