International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 4, Pages 715-720
doi:10.1155/S0161171282000659
On the Hardy-Littlewood maximal theorem
Shinji Yamashita
Department of Mathematics, Tokyo Metropolitan University, Fukazawa, Setagaya, Tokyo 158, Japan
Abstract
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.