论文标题
多线性紧凑型操作员和应用的外推
Extrapolation for multilinear compact operators and applications
论文作者
论文摘要
本文致力于研究多线性紧凑型操作员的卢比奥弗朗西亚外推。它可以将$ t $从一个空间推断到整个加权空间的紧凑性，每当$ m $ - 线性运算符$ t $都在加权的lebesgue空间上。确实，该结果是根据多线Muckenhoupt toges $ a _ {\ vec {p}，\ vec {r}} $建立的，以及$ l^p $ scale的有限范围。为了通过新的加权Fréchet-Kolmogorov定理显示外推理，我们为多连接紧凑型操作员提供了加权插值。为了证明后者，我们还需要在混合 - 纳尔姆·勒布斯格空间中进行加权插值定理。作为应用程序，我们获得了许多多线性操作员的换向器的加权紧凑性，包括多线性$ω$-CALDERón-Zygmund运算符，多线性傅立叶乘数，双线性粗糙的奇异积分和双线性Bochner-Riesz的含义。除此之外，我们还建立了高级Calderón换向因子的加权紧凑性，以及与Schrödinger运营商相关的Riesz的换向器。
This paper is devoted to studying the Rubio de Francia extrapolation for multilinear compact operators. It allows one to extrapolate the compactness of $T$ from just one space to the full range of weighted spaces, whenever an $m$-linear operator $T$ is bounded on weighted Lebesgue spaces. This result is indeed established in terms of the multilinear Muckenhoupt weights $A_{\vec{p}, \vec{r}}$, and the limited range of the $L^p$ scale. To show extrapolation theorems above, by means of a new weighted Fréchet-Kolmogorov theorem, we present the weighted interpolation for multilinear compact operators. To prove the latter, we also need to bulid a weighted interpolation theorem in mixed-norm Lebesgue spaces. As applications, we obtain the weighted compactness of commutators of many multilinear operators, including multilinear $ω$-Calderón-Zygmund operators, multilinear Fourier multipliers, bilinear rough singular integrals and bilinear Bochner-Riesz means. Beyond that, we establish the weighted compactness of higher order Calderón commutators, and commutators of Riesz transforms related to Schrödinger operators.
