论文标题
$σ$ -finite von neumann代数和傅立叶乘数$ su_q（2）$的BMO空间
BMO spaces of $σ$-finite von Neumann algebras and Fourier-Schur multipliers on $SU_q(2)$
论文作者
论文摘要
我们考虑与任意$σ$ -finite von Neumann代数$（\ Mathcal {M}，φ）$相关的半组BMO空间。我们证明相关的行和列BMO空间始终承认有限案例的结果。因此，我们可以证明所考虑的半集体BMO空间是Banach的空间，它们与$ L_P $插值一样，如通勤情况，即$ [\ MATHRM {BMO}（\ Mathcal {M {M}） l_ {pq}^\ circ（\ mathcal {m}）$。然后，我们研究新的示例。我们在紧凑型量子组上介绍了傅立叶速度乘数的概念，并表明这种乘数自然存在于$ su_q（2）$。
We consider semi-group BMO spaces associated with an arbitrary $σ$-finite von Neumann algebra $(\mathcal{M}, φ)$. We prove that the associated row and column BMO spaces always admit a predual, extending results from the finite case. Consequently, we can prove that the semi-group BMO spaces considered are Banach spaces and they interpolate with $L_p$ as in the commutative situation, namely $[\mathrm{BMO}(\mathcal{M}), L_p^\circ(\mathcal{M})]_{1/q} \approx L_{pq}^\circ(\mathcal{M})$. We then study a new class of examples. We introduce the notion of Fourier-Schur multiplier on a compact quantum group and show that such multipliers naturally exist for $SU_q(2)$.
