Hardy-Littlewood-Paley inequalities and Fourier multipliers on SU(2)
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Published version
Author(s)
Ruzhansky, M
Akylzhanov, R
Nursultanov, E
Type
Journal Article
Abstract
We prove noncommutative versions of Hardy–Littlewood and Paley inequalities
relating a function and its Fourier coefficients on the group SU(2). We use it
to obtain lower bounds for the L
p
-L
q norms of Fourier multipliers on SU(2) for 1 < p ≤
2 ≤ q < ∞. 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).
relating a function and its Fourier coefficients on the group SU(2). We use it
to obtain lower bounds for the L
p
-L
q norms of Fourier multipliers on SU(2) for 1 < p ≤
2 ≤ q < ∞. 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
2016-06-17
Date Acceptance
2016-04-21
Citation
Studia Mathematica, 2016
ISSN
1730-6337
Publisher
Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics)
Journal / Book Title
Studia Mathematica
Copyright Statement
© Instytut Matematyczny PAN, 2016
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/K039407/1
Subjects
0101 Pure Mathematics
Publication Status
Accepted