Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group
نویسندگان
چکیده
We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group Γ and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum Λ ⊆ Γ , the norm of the Hilbert transform and the Riesz projection on Schatten-vonNeumann classes with exponent a power of 2, and the norm of Toeplitz Schur multipliers on Schatten-von-Neumann classes with exponent less than 1.
منابع مشابه
Characterization of finite $p$-groups by the order of their Schur multipliers ($t(G)=7$)
Let $G$ be a finite $p$-group of order $p^n$ and $|{mathcal M}(G)|=p^{frac{1}{2}n(n-1)-t(G)}$, where ${mathcal M}(G)$ is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer. The classification of such groups $G$ is already known for $t(G)leq 6$. This paper extends the classification to $t(G)=7$.
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