$\mathbb C ^{2n}$中乘积域Shilov边界上Kohn Laplacian的Marcinkiewicz乘子
Marcinkiewicz multipliers associated with the Kohn Laplacian on the Shilov boundary of the product domain in $\mathbb C ^{2n}$
摘要：
设$M^{(k)}$，$k=1,2,\ldots, n$是$\mathbb C ^2$中有限型无界多项式域$Ω^{(k)}$的边界，$\Box_b^{(k)}$是$M^{(k)}$上的Kohn Laplacian.本文研究了作用在乘积域$Ω^{(1)}\times\cdots\times Ω^{(n)}$的Shilov边界$\widetilde{M}=M^{(1)} \times\cdots\times M^{(n)}$上的多元谱乘子$m(\Box_b^{(1)},\ldots, \Box_b^{(n)})$。证明了如果函数$F(λ_1, \ldots ,λ_n)$满足Marcinkiewicz型微分条件，则谱乘子算子$m(\Box_b^{(1)}, \ldots, \Box_b^{(n)})$是Journé型的乘积Calderon-Zygmund算子.
英文摘要：
Let $M^{(k)}$, $k=1,2,\ldots, n$, be the boundary of an unbounded polynomial domain $Ω^{(k)}$ of finite type in $\mathbb C ^2$, and let $\Box_b^{(k)}$ be the Kohn Laplacian on $M^{(k)}$. In this paper, we study multivariable spectral multipliers $m(\Box_b^{(1)},\ldots, \Box_b^{(n)})$ acting on the Shilov boundary $\widetilde{M}=M^{(1)} \times\cdots\times M^{(n)}$ of the product domain $Ω^{(1)}\times\cdots\times Ω^{(n)}$. We show that if a function $F(λ_1, \ldots ,λ_n)$ satisfies a Marcinkiewicz-type differential condition, then the spectral multiplier operator $m(\Box_b^{(1)}, \ldots, \Box_b^{(n)})$ is a product Calderón--Zygmund operator of Journé type.
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