TY - JOUR

T1 - Variation of CalderónZygmund operators with matrix weight

AU - Duong, Xuan Thinh

AU - Li, Ji

AU - Yang, Dongyong

PY - 2020/10/24

Y1 - 2020/10/24

N2 - 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.

AB - 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.

KW - CalderónZygmund operator

KW - variation

KW - matrix weight

KW - sparse operator

UR - http://www.scopus.com/inward/record.url?scp=85095434179&partnerID=8YFLogxK

U2 - 10.1142/S0219199720500625

DO - 10.1142/S0219199720500625

M3 - Article

AN - SCOPUS:85095434179

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

ER -