Journal of Function Spaces and Applications (Jan 2012)
BMO-Boundedness of Maximal Operators and g-Functions Associated with Laguerre Expansions
Abstract
Let {ππΌπ}πββ be the Laguerre functions of Hermite type with index πΌ. These are eigenfunctions of the Laguerre differential operator πΏπΌ=1/2(βπ2/ππ¦2+π¦2+ξ·1/π¦2ξΈ(πΌ2β1/4)). In this paper, we investigate the boundedness of the Hardy-Littlewood maximal function, the heat maximal function, and the Littlewood-Paley π-function associated with πΏπΌ in the localized BMO space BMOπΏπΌ, which is the dual space of the Hardy space π»1πΏπΌ.