In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators Tbm. Our results are new even for the first order commutator Tb1. A new bump type necessary condition for the two-weighted boundedness of Tbm is obtained as well. We also provide some results related to a converse to Bloom's theorem.
Bibliographical noteFunding Information:
The first author was supported by ISF grant No. 447/16 and ERC Starting Grant No. 713927 . The second and third authors were supported by CONICET PIP 11220130100329CO and Agencia I+D+i PICT 2018-02501 . The third author was supported by Agencia I+D+i PICT 2019-00018 .
© 2021 Elsevier Inc.
- Calderón-Zygmund operators
- Sparse operators
- Weighted inequalities