Littlewood-Paley <inline-formula> <graphic file="1029-242X-2011-741095-i1.gif"/></inline-formula>-Functions and Multipliers for the Laguerre Hypergroup

• Main Author: Huang Jizheng
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2011/741095
• ISSN: 1025-5834; 1029-242X

<p>Abstract</p> <p>Let <inline-formula> <graphic file="1029-242X-2011-741095-i2.gif"/></inline-formula><inline-formula> <graphic file="1029-242X-2011-741095-i3.gif"/></inline-formula> where <inline-formula> <graphic file="1029-242X-2011-741095-i4.gif"/></inline-formula>. Then <inline-formula> <graphic file="1029-242X-2011-741095-i5.gif"/></inline-formula> can generate a hypergroup which is called Laguerre hypergroup, and we denote this hypergroup by <b>K</b>. In this paper, we will consider the Littlewood-Paley <inline-formula> <graphic file="1029-242X-2011-741095-i6.gif"/></inline-formula>-functions on <b>K</b> and then we use it to prove the H&#246;lmander multipliers on <b>K</b>.</p>