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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 923874, 21 pages
http://dx.doi.org/10.1155/2012/923874
Research Article

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

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

Received 29 February 2012; Revised 21 May 2012; Accepted 21 June 2012

Academic Editor: Aurelian Gheondea

Copyright © 2012 Li Cha and Heping Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let { πœ‘ 𝛼 𝑛 } 𝑛 ∈ β„• be the Laguerre functions of Hermite type with index 𝛼 . These are eigenfunctions of the Laguerre differential operator 𝐿 𝛼 = 1 / 2 ( βˆ’ 𝑑 2 / 𝑑 𝑦 2 + 𝑦 2 + ξ€· 1 / 𝑦 2 ξ€Έ ( 𝛼 2 βˆ’ 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 𝐿 𝛼 in the localized BMO space B M O 𝐿 𝛼 , which is the dual space of the Hardy space 𝐻 1 𝐿 𝛼 .