Weighted estimates for commutators of anisotropic Calderón-Zygmund operators. Issue 4 (4th March 2022)

• Record Type: Journal Article
• Authors: Li, Jinxia; He, Jianxun
• Is Part Of: Applicable analysis. Volume 101:Issue 4(2022)
• Page Start: 1299
• Page End: 1314
• Publication Date: 2022-03-04
• Subjects: J. Shi; Expansive dilation -- Muckenhoupt weights -- weighted Hardy spaces -- Calderón-Zygmund operators -- commutators; 42B35 -- 46E30 -- 42B25 -- 42B30; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1779230
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : Let T be an anisotropic Calderón-Zygmund operator and b ∈ L i p α, w ( R n, A ) with 0 < α < 1 and L i p α, w ( R n, A ) being an anisotropic weighted Lipschitz space. The goal of the paper is to give five boundedness theorems of the commutator [ b, T ] . Precisely, [ b, T ] is bounded from L w q ( R n ) to L w 1 − q r q r ( R n ), where w ∈ A q r ( A ), 1 / q r = 1 / q − α / n, 1 < q < n / α and 1 < r < ∞ ; [ b, T ] is bounded from L w q ( R n ) to L w 1 − r r ( R n ), when w ∈ A 1 ( A ) or w ∈ A r ( A ), 1 / r = 1 / q − α / n, 1 < q < n / α and 1 < q < r < ∞ ; [ b, T ] is bounded from anisotropic weighted Hardy space H w p ( R n, A ) to L w 1 − r r ( R n ), if w ∈ A 1 ( A ) or w ∈ A r ( A ), 1 / r = 1 / p − α / n and n / ( n + α ) < p ≤ 1 < r < ∞ ; [ b, T ] is bounded from H w n / ( n + α ) ( R n, A ) to weak Lebesgue space L 1, ∞ ( R n ) with w ∈ A 1 ( A ), p = n / ( n + α ), which are extensions of isotropic settings and new even for the isotropic weighted and anisotropic unweighted settings.