TY - JOUR
T1 - $H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II
AU - T. Kawazoe
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 - <p style="text-align: justify;">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.</p>