$H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II (Analysis in Theory and Applications, 2016)
Let $({\Bbb R}_+,*,Δ)$ 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 $({\Bbb R}_+,*,Δ)$ 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.
Keywords: Jacobi analysis; Jacobi hypergroup; $g$ function; area function; real Hardy space.