Variation of CalderónZygmund operators with matrix weight

Xuan Thinh Duong, Ji Li*, Dongyong Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let p (1,∞), ρ (2,∞) and W be a matrix Ap weight. In this paper, we introduce a version of variation ρ(n, ) for matrix CalderónZygmund operators with modulus of continuity satisfying the Dini condition. We then obtain the Lp(W)boundedness of ρ(n, ) with norm ρ(n, )Lp(W)→Lp(W) ≤ C[W]Ap1+ 1 p1 1 p by first proving a sparse domination of the variation of the scalar CalderónZygmund operator, and then providing a convex body sparse domination of the variation of the matrix CalderónZygmund operator. The key step here is a weak type estimate of a local grand maximal truncated operator with respect to the scalar CalderónZygmund operator.

Original languageEnglish
JournalCommunications in Contemporary Mathematics
Early online date24 Oct 2020
DOIs
Publication statusE-pub ahead of print - 24 Oct 2020

Keywords

  • CalderónZygmund operator
  • variation
  • matrix weight
  • sparse operator

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