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A pair of dual frames with almost exponentially localized elements (needlets)are constructed on $\RR_+^d$ based on Laguerre functions. It is shown that theTriebel-Lizorkin and Besov spaces induced by Laguerre expansions can becharacterized in terms of respective sequence spaces that involve the needletcoefficients.

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