论文标题
自由组的热量平滑剂量的自由组von Neumann代数
Heat-smoothing for holomorphic subalgebras of free group von Neumann algebras
论文作者
论文摘要
离散高管上的热量半群众所周知，$ 1 <p <\ infty $的$ l_p $ spaces均超过$ l_p $。 Mendel和Naor \ cite {Mn14}的问题涉及尾部空间中更强的收缩特性，这被称为热平滑的猜想。 Eskenazis和Ivanisvili \ cite {ei20}考虑了这种猜想的高斯类似物，并解决了一些特殊情况。特别是，他们证明了热平滑型的猜想可用于具有锋利常数的高斯空间中的全态功能。在本文中，我们证明了对自由组von Neumann代数的霍明型亚代数的类似尖锐不平等。类似的结果也适用于$ Q $ -Gaussian代数和量子托里。对于自由组von Neumann代数，通过最佳秩序证明了热平滑的表述较弱。
The heat semigroup on discrete hypercubes is well-known to be contractive over $L_p$-spaces for $1<p<\infty$. A question of Mendel and Naor \cite{MN14} concerns a stronger contraction property in the tail spaces, which is known as the heat-smoothing conjecture. Eskenazis and Ivanisvili \cite{EI20} considered a Gaussian analog of this conjecture and resolved some special cases. In particular, they proved that heat-smoothing type conjecture holds for holomorphic functions in the Gaussian spaces with sharp constants. In this paper, we prove analogous sharp inequalities for holomorphic subalgebras of free group von Neumann algebras. Similar results also hold for $q$-Gaussian algebras and quantum tori. In the case of free group von Neumann algebras, the weaker formulation of heat-smoothing is proved with optimal order.
