Weighted estimates for maximal bilinear rough singular integrals via sparse dominations
Collectanea Mathematica - 2021
Tóm tắt
Let
$$x=(x_1,x_2)$$
with
$$x_1,x_2 \in \mathbb {R}^n$$
and let
$$K(x)={\Omega \big ({x}/{|x|}\big )}{\big |x\big |^{-2n}}$$
, where
$$\Omega \in L^{\infty }(\mathbb {S}^{2n-1})$$
and satisfies
$$\int _{\mathbb {S}^{2n-1}}\Omega =0$$
. We show that the maximal truncated bilinear singular integrals with rough kernel
$$K(x_1,x_2)$$
satisfy a sparse bound by (p, p, p)-averages for all
$$p>1$$
. As consequences, we obtain some quantitative weighted estimates for these rough singular integrals. A pointwise sparse domination for commutators of bilinear rough singular integrals were also established, which can be used to establish some weighted inqualities.
Từ khóa
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