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Let {}∈ℕ be the Laguerre functions of Hermite type with index . These are eigenfunctions of the Laguerre differential operator =1/2(−2/2+2+1/2(2−1/4)). In this paper, we investigate the boundedness of the Hardy-Littlewood maximal function, the heat maximal function, and the Littlewood-Paley -function associated with  in the localized BMO space BMO, which is the dual space of the Hardy space 1

BMO-Boundedness of Maximal Operators andg-Functions Associated with Laguerre Expansions