Abstract
The Hardy–Littlewood inequality on the circle group compares the -norm of a function with a weighted -norm of its sequence of Fourier coefficients. The approach has recently been explored for compact homogeneous spaces and we study a natural analogue in the framework of compact quantum groups. In particular, in the case of the reduced group -algebras and free quantum groups, we establish explicit inequalities through inherent information of the underlying quantum groups such as growth rates and the rapid decay property. Moreover, we show sharpness of the inequalities in a large class, including a compact Lie group, with a polynomially growing discrete group and free quantum groups , .
Citation
Sang-Gyun Youn. "Hardy–Littlewood inequalities on compact quantum groups of Kac type." Anal. PDE 11 (1) 237 - 261, 2018. https://doi.org/10.2140/apde.2018.11.237
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