论文标题
加权空间上的紧凑性外推：非对角线和有限的范围估计值
Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates
论文作者
论文摘要
在我们一个人的一篇论文中，证明了卢比亚·弗朗西亚（Rubio de Francia）加权推断定理的“紧凑版”，这使一个人可以推断操作员的紧凑性从仅一个空间到整个加权空间，而该操作员的界限。在本文中，我们为从一个空间到另一个空间（“偏外估计”）或仅在有限的$ l^p $ scale范围内获得了这种紧凑性的推断。作为应用程序，我们很容易地恢复有关分数积分和伪差异操作员的加权紧凑性的最新结果，并获得有关Bochner-Riesz乘数加权紧凑性的新结果。
In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operator from just one space to the full range of weighted spaces, where this operator is bounded. In this paper, we obtain generalizations of this extrapolation of compactness for operators that are bounded from one space to a different one ("off-diagonal estimates") or only in a limited range of the $L^p$ scale. As applications, we easily recover recent results on the weighted compactness of commutators of fractional integrals and pseudo-differential operators, and obtain new results about the weighted compactness of Bochner--Riesz multipliers.
