Hardy Spaces For Laguerre Expansions

The Hardy space HL1associated with the Laguerre operator L is studied in this paper. Under certain conditions, HL1is characterized by the Littlewood-Paley g-function related to the Laguerre operator L, which is stated in theorem1. Some results about the Hardy space associated with Hermite expansions are got. Finally, the boundedness of Riesz transformation associated with Hermite expansions in the Hardy space and the boundedness of Riesz transformation associated with Laguerre expansions in the Hardy space HL1are proved.Firstly, the meaning and status of the Hardy space and the content and the structure arrangement of this paper are given.Secondly, the definition of the Hardy space and same equivalent characterizations are given.Thirdly, characterization of the Hardy space associated with Laguerre expansion is given.Next, boundedness of Riesz transforms associated with Laguerre expansion on the Hardy space is proved.Lastly, research results and prospects of this paper are given.