On the mixed radial-angular integrability of Littlewood-Paley functions
Bull. Korean Math. Soc. 2021 Vol. 58, No. 2, 403-417
https://doi.org/10.4134/BKMS.b200318
Published online September 3, 2020
Printed March 31, 2021
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 function, weighted norm inequality, mixed radial-angular space
MSC numbers : Primary 42B25, 42B20
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