1Department of Mathematics, Guangdong Education Institute, and Guangzhou, Guangdong 510303, P. R. China
2Zagoras St. Paradissos, Amaroussion 15125 Athens, Greece
3Department of Mathematics, National Technical University of Athens, Zografou, Campus 15780 Athens, Greece
In this paper, we reconstruct the Hardy-Littlewood’s inequality by using the method of the weight coefficient and the technic of real analysis including a best constant factor. An open problem is raised.