论文标题
Marcinkiewicz乘数与Kohn Laplacian在$ \ Mathbb C ^{2n} $中的Shilov边界上的Kohn Laplacian关联
Marcinkiewicz multipliers associated with the Kohn Laplacian on the Shilov boundary of the product domain in $\mathbb C ^{2n}$
论文作者
论文摘要
令$ m^{（k）} $，$ k = 1,2，\ ldots，n $，为有限的多项式域$ \ mathbb c^2 $的无限多项式域$ω^{（k）} $，以及Let $ \ box_b^{（k）$ a $ kohn laplaclacian $ n laplacian。在本文中，我们研究了多变光谱乘数$ m（\ box_b^{（1）}，\ ldots，\ box_b^{（n）}）$在Shilov边界$ \ wideTilde {m} = m} = m^{（1）} \ cdots \ cdots \ cdots \ cdots \ cdips \ times m^{（n） $ω^{（1）} \ times \ cdots \ timesω^{（n）} $。我们表明，如果功能$ f（λ_1，\ ldots，λ_n）$满足marcinkiewicz-type差异条件，则频谱乘数运算符$ m（\ box_b^{（1）}，\ ldots，\ box_b^{（n）} $是floges calderewor caldereworn--zygmund-jooker-jooder-jooky-kygmund jookygmund-
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.
