Extrapolation of compactness on weighted spaces II: Off-diagonal and limited range estimates
arXiv:2006.15858
Abstract
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 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.
arXiv commentv2: We corrected a typo at the end of the proof of Lemma 3.4 and an oversight in the proof of Lemma 3.7, 24 pages. arXiv admin note: substantial text overlap with arXiv:2003.01606
References in corpus (4)
- Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights
- Boundedness results for commutators with BMO functions via weighted estimates: a comprehensive approach
- A revisit on the compactness of commutators
- Extrapolation of compactness on weighted spaces