Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2) | Zendy

Rauan Akylzhanov | Zendy; Erlan Nurlustanov | Zendy; Michael Ruzhansky | Zendy

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Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2)

Author(s) -

Rauan Akylzhanov,

Erlan Nurlustanov,

Michael Ruzhansky

Publication year - 2016

Publication title -

studia mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.954

H-Index - 55

eISSN - 1730-6337

pISSN - 0039-3223

DOI - 10.4064/sm8106-4-2016

Subject(s) - mathematics , noncommutative geometry , fourier transform , noncommutative harmonic analysis , inequality , pure mathematics , fourier series , function (biology) , hardy space , combinatorics , mathematical analysis , lie group , compact group , evolutionary biology , biology

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)

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