Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2)
Studia Mathematica, Tome 234 (2016) no. 1, pp. 1-29
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 ${\rm SU(2)}$.
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
Affiliations des auteurs :
Rauan Akylzhanov 1 ; Erlan Nursultanov 2 ; Michael Ruzhansky 1 ; Erlan Nursultanov 2
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author = {Rauan Akylzhanov and Erlan Nursultanov and Michael Ruzhansky and Erlan Nursultanov},
title = {Hardy{\textendash}Littlewood{\textendash}Paley inequalities and {Fourier} multipliers on {SU(2)}},
journal = {Studia Mathematica},
pages = {1--29},
publisher = {mathdoc},
volume = {234},
number = {1},
year = {2016},
doi = {10.4064/sm8106-4-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8106-4-2016/}
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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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