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2018 Hardy–Littlewood inequalities on compact quantum groups of Kac type
Sang-Gyun Youn
Anal. PDE 11(1): 237-261 (2018). DOI: 10.2140/apde.2018.11.237

Abstract

The Hardy–Littlewood inequality on the circle group T compares the Lp-norm of a function with a weighted p-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 C-algebras and free quantum groups, we establish explicit Lpp 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 G a compact Lie group, Cr(G) with G a polynomially growing discrete group and free quantum groups ON+, SN+.

Citation

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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

Information

Received: 16 February 2017; Revised: 16 June 2017; Accepted: 24 July 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 06789265
MathSciNet: MR3707297
Digital Object Identifier: 10.2140/apde.2018.11.237

Subjects:
Primary: 20G42, 43A15, 46L51, 46L52

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 1 • 2018
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