TY - JOUR T1 - $H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II JO - Analysis in Theory and Applications VL - 1 SP - 38 EP - 51 PY - 2016 DA - 2016/01 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n1.4 UR - https://global-sci.org/intro/article_detail/ata/4653.html KW - Jacobi analysis, Jacobi hypergroup, $g$ function, area function, real Hardy space. AB -

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.