Our aim is to characterize the elements in certain function spaces by means of the Ces\'aro means and/or partial sums of their Fourier series. Firstly, we seek to extend known results for the Besov spaces to the case where . Secondly, we consider the Mean Lipschitz spaces . We confine attention to the values and for the parameters. For , the spaces and coincide. For the case certain counter-examples are provided; some positive results are also given. We then treat the case and consider the spaces and separately. Analogues of some known results for the spaces are given.
Cite this article
D. Walsh, Criteria for Membership of the Mean Lipschitz Spaces. Z. Anal. Anwend. 22 (2003), no. 2, pp. 339–355DOI 10.4171/ZAA/1149