论文标题
加权空间的紧凑性外推：双线性操作员
Extrapolation of compactness on weighted spaces: Bilinear operators
论文作者
论文摘要
在上一篇论文中，我们获得了卢比亚·弗朗西亚（Rubio de Francia）的加权推断定理的几个“紧凑型版本”，这使我们能够推断线性操作员的紧凑性从仅一个空间到整个加权的Lebesgue空间，这些操作员在这些空间中界定了这些操作员的边界。在本文中，我们研究了双线性算子的紧凑性的外推，从双线性粉状的重量来看。作为应用，我们轻松地恢复并改善了对双线性Calderón-Zygmund运算符，双线性分数积分和双线性傅立叶乘数的换向器的加权紧凑型的早期结果。这些结果的更一般版本最近是由于CAO，Olivo和Yabuta（Arxiv：2011.13191），其方法取决于开发Fréchet的加权版本-Kolmogorov紧凑性的标准，而我们避免了这种依赖于“ SOSOFTER”工具的避免这种方法，该工具可以独立于进一步的扩展，该工具可以进行进一步扩展的方法。
In a previous paper, we obtained several "compact versions" of Rubio de Francia's weighted extrapolation theorem, which allowed us to extrapolate the compactness of linear operators from just one space to the full range of weighted Lebesgue spaces, where these operators are bounded. In this paper, we study the extrapolation of compactness for bilinear operators in terms of bilinear Muckenhoupt weights. As applications, we easily recover and improve earlier results on the weighted compactness of commutators of bilinear Calderón-Zygmund operators, bilinear fractional integrals and bilinear Fourier multipliers. More general versions of these results are recently due to Cao, Olivo and Yabuta (arXiv:2011.13191), whose approach depends on developing weighted versions of the Fréchet--Kolmogorov criterion of compactness, whereas we avoid this by relying on "softer" tools, which might have an independent interest in view of further extensions of the method.
