On the mixed radial-angular integrability of Littlewood-Paley functions
Bull. Korean Math. Soc.
Published online September 3, 2020
Xiao Zhang
Shandong University of Science and Technology
Abstract : This note is devoted to establishing the boundedness
for some classes of Littlewood-Paley square operators defined by the
kernels without any regularity on the mixed radial-angular spaces.
The corresponding vector-valued versions are also presented. As
applications, the corresponding results for the Littlewood-Paley
$g_{\lambda}^{*}$ function and the Littlewood-Paley function related
to the area integrals are also obtained.
Keywords : Littlewood-Paley functions, weighted norm inequalities, mixed radial-angular spaces.
MSC numbers : 42B25, 42B20
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