New oscillation classes and two weight bump conditions for commutators
-
Cruz Uribe, David [1] ; Moen, Kabe [1] ; Minh Tran, Quan [1]
-
[1] Department of Mathematics, University of Alabama, Tuscaloosa, 35487, USA
-
- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 1, 2023, págs. 225-246
- Idioma: inglés
- DOI: 10.1007/s13348-021-00344-3
- Texto completo no disponible (Saber más ...)
-
Resumen
In this paper we consider two weight bump conditions for higher order commutators. Given b and a Calderón–Zygmund operator T, define the commutator T1bf=[T,b]f=bTf−T(bf), and for m≥2 define the iterated commutator Tmbf=[b,Tm−1b]f. Traditionally, commutators are defined for functions b∈BMO, but we show that if we replace BMO by an oscillation class first introduced by Pérez (J Funct Anal 128(1):163–185, 1995), we can give a range of sufficient conditions on a pair of weights (u, v) for Tmb:Lp(v)→Lp(u) to be bounded. Our results generalize work of Cruz-Uribe and Moen (Publ Mat 56(1):147–190, 2012), and more recent work by Lerner et al. (J Funct Anal 281(8):46, 2021). We also prove necessary conditions for the iterated commutators to be bounded, generalizing results of Isralowitz et al. (Commutators in the two scalar and matrix weighted setting. Preprint, 2020. http://arxiv.org/abs/2001.11182).
