BMO-Boundedness of Maximal Operators and g-Functions Associated with Laguerre Expansions

Abstract EN

Let {φnα}n∈ℕ be the Laguerre functions of Hermite type with index α.

These are eigenfunctions of the Laguerre differential operator Lα=1/2(-d2/dy2+y2+(1/y2)(α2-1/4)).

In this paper, we investigate the boundedness of the Hardy-Littlewood maximal function, the heat maximal function, and the Littlewood-Paley g-function associated with Lα in the localized BMO space BMOLα, which is the dual space of the Hardy space HLα1.