International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 4, Pages 715-720

On the Hardy-Littlewood maximal theorem

Shinji Yamashita

Department of Mathematics, Tokyo Metropolitan University, Fukazawa, Setagaya, Tokyo 158, Japan

Received 5 May 1981

Copyright © 1982 Shinji Yamashita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Hardy-Littlewood maximal theorem is extended to functions of class PL in the sense of E. F. Beckenbach and T. Radó, with a more precise expression of the absolute constant in the inequality. As applications we deduce some results on hyperbolic Hardy classes in terms of the non-Euclidean hyperbolic distance in the unit disk.