@Article{ATA-32-38, author = {}, title = {$H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {1}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n1.4}, url = {http://global-sci.org/intro/article_detail/ata/4653.html} }