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

Abstract

Let {𝜑𝛼𝑛}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 𝐻1𝐿𝛼.