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Let p (1,∞), ρ (2,∞) and W be a matrix Ap weight. In this paper, we introduce a version of variation Vρ(Tn, - ∗) for matrix Calderón-Zygmund operators with modulus of continuity satisfying the Dini condition. We then obtain the Lp(W)-boundedness of Vρ(Tn, - ∗) with norm (equation presented) by first proving a sparse domination of the variation of the scalar Calderón-Zygmund operator, and then providing a convex body sparse domination of the variation of the matrix Calderón-Zygmund operator. The key step here is a weak type estimate of a local grand maximal truncated operator with respect to the scalar Calderón-Zygmund operator.
|Number of pages||30|
|Journal||Communications in Contemporary Mathematics|
|Early online date||24 Oct 2020|
|Publication status||Published - Nov 2021|
- CalderónZygmund operator
- matrix weight
- sparse operator
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Harmonic analysis and dispersive partial differential equations
Li, J., Guo, Z., Kenig, C. & Nakanishi, K.
31/01/17 → …
Harmonic analysis: function spaces and partial differential equations
Duong, X., Hofmann, S., Ouhabaz, E. M. & Wick, B.
11/02/19 → 10/02/22