(untitled) (Analysis in Theory and Applications, 2016)
Let (R_+,*,Δ) 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 (R_+,*,Δ) 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.