Geodesic
Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2)
Rauan Akylzhanov1 ; Erlan Nursultanov2 ; Michael Ruzhansky1 ; Erlan Nursultanov2
1Department of Mathematics Imperial College London 180 Queen’s Gate London SW7 2AZ, United Kingdom
2Department of Mathematics Moscow State University, Kazakh Branch Astana, Kazakhstan
Studia Mathematica, Tome 234 (2016) no. 1, pp. 1-29
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We prove noncommutative versions of Hardy–Littlewood and Paley inequalities relating a function and its Fourier coefficients on the group ${\rm SU(2)}$. We use it to obtain lower bounds for the $L^p$-$L^q$ norms of Fourier multipliers on ${\rm SU(2)}$ for $1 \lt p\leq 2\leq q \lt \infty $. 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 ${\rm SU(2)}$.
DOI : 10.4064/sm8106-4-2016
Keywords: prove noncommutative versions hardy littlewood paley inequalities relating function its fourier coefficients group obtain lower bounds p l norms fourier multipliers leq leq infty addition upper bounds similar form analogous known results torus noncommutative setting

Rauan Akylzhanov  1   ; Erlan Nursultanov  2   ; Michael Ruzhansky  1   ; Erlan Nursultanov  2

1 Department of Mathematics Imperial College London 180 Queen’s Gate London SW7 2AZ, United Kingdom
2 Department of Mathematics Moscow State University, Kazakh Branch Astana, Kazakhstan 
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Rauan Akylzhanov; Erlan Nursultanov; Michael Ruzhansky; Erlan Nursultanov. Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2). Studia Mathematica, Tome 234 (2016) no. 1, pp. 1-29. doi: 10.4064/sm8106-4-2016

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