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arXiv · 1403.1731

Hardy-Littlewood inequalities and Fourier multipliers on SU(2)

Rauan Akylzhanov·Erlan Nursultanov·Michael Ruzhansky
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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 $SU(2)$.

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Rauan Akylzhanov, Erlan Nursultanov, Michael Ruzhansky. 2014-03-07. Hardy-Littlewood inequalities and Fourier multipliers on SU(2). https://arxiv.org/abs/1403.1731

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