Improved $A_1-A_{\infty }$ and related estimates for commutators of rough singular integrals

Abstract

An $A_1-A_{\infty }$ estimate improving a previous result in arXiv:1607.06432 is obtained. Also new a result in terms of the $A_{\infty }$ constant and the one supremum $A_q-A_{\infty }^{\exp }$ constant, is proved, providing a counterpart for the result obained in arXiv:1705.08364. Both of the preceding results rely upon a sparse domination in terms of bilinear forms for $[b,T_{\Omega }]$ with $\Omega \in L^{\infty }({\mathbb{S}}^{n-1})$ and $b\in BMO$ which is established relying upon techniques from arXiv:1705.07397.

Some typos and misprints corrected

References in corpus (1)

• A sparse domination principle for rough singular integrals

Cited by in corpus (2)

• Bloom weighted bounds for sparse forms associated to commutators
• Two-weight extrapolation on function spaces and applications