Year: 2016
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 38–51
Abstract
Let $({\Bbb R}_+,*,\Delta)$ be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley $g$ function and the Lusin area function for the Jacobi hypergroup and consider their $(H^1, L^1)$ boundedness. Although the $g$ operator for $({\Bbb R}_+,*,\Delta)$ possesses better property than the classical $g$ operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the $(H^1, L^1)$ estimate for the Lusin area operator, a slight modification in its form is required.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2016.v32.n1.4
Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 38–51
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Jacobi analysis Jacobi hypergroup $g$ function area function real Hardy space.