Decomposition of Triebel–Lizorkin and Besov spaces in the context of Laguerre expansions

A pair of dual frames with almost exponentially localized elements (needlets) are constructed on based on Laguerre functions. It is shown that the Triebel–Lizorkin and Besov spaces induced by Laguerre expansions can be characterized in terms of respective sequence spaces that involve the needlet coefficients.