Hardy-Littlewood inequalities and Fourier multipliers on SU(2)
File(s)1403.1731v1.pdf (303.01 KB)
Accepted version
Author(s)
Akylzhanov, R
Nursultanov, E
Ruzhansky, M
Type
Working Paper
Abstract
In this paper we prove a noncommutative version of Hardy-Littlewood
inequalities relating a function and its Fourier coefficients on the group
SU(2). As a consequence, we use it to obtain lower bounds for the L^p-L^q
norms of Fourier multipliers on the group SU(2), for 1 < p \leq 2 \leq q <
1. In addition, we give upper bounds of a similar form, analogous to the known results on the torus, but now in the noncommutative setting of SU(2).
inequalities relating a function and its Fourier coefficients on the group
SU(2). As a consequence, we use it to obtain lower bounds for the L^p-L^q
norms of Fourier multipliers on the group SU(2), for 1 < p \leq 2 \leq q <
1. In addition, we give upper bounds of a similar form, analogous to the known results on the torus, but now in the noncommutative setting of SU(2).
Date Issued
2015-10-23
Citation
2015
Copyright Statement
© 2015 the Authors
Identifier
http://arxiv.org/abs/1403.1731v2
Subjects
Functional Analysis
Publication Status
Published
Publisher URL