Copyright © 2011 Jizheng Huang. 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.
Let where . Then can generate a hypergroup which is called Laguerre hypergroup, and we denote this hypergroup by K. In this paper, we will consider the Littlewood-Paley -functions on K and then we use it to prove the Hölmander multipliers on K.