论文标题
粗糙双线性单数积分的稀疏支配和加权估计值
Sparse domination and weighted estimates for rough bilinear singular integrals
论文作者
论文摘要
令$ r> \ frac {4} {3} $，让$ω\ in l^{r}（\ mathbb {s}^{2n-1}）$具有消失的积分。我们表明双线性粗糙的奇异积分$$t_Ω（f，g）（x）= \ textrm {p.v。} \ int _ {\ Mathbb {r}^n} \ int _ {\ Mathbb {r}^n}^n} \ frac {ω（y，z）/|（y，z）|（y，z）}} {|（y，z）|（y，z） $（p，p，p）$ - 平均值，其中$ p $大于与$ r $和$ n $明确相关的一定数量。结果，我们推断出与粗糙均匀核相关的双线性均匀奇异积分的某些定量加权估计。
Let $r>\frac{4}{3}$ and let $Ω\in L^{r}(\mathbb{S}^{2n-1})$ have vanishing integral. We show that the bilinear rough singular integral $$T_Ω(f,g)(x)= \textrm{p.v.} \int_{\mathbb{R}^n}\int_{\mathbb{R}^n}\frac{Ω((y,z)/|(y,z)|)}{|(y,z)|^{2n}}f(x-y)g(x-z)\,dydz,$$ satisfies a sparse bound by $(p,p,p)$-averages, where $p$ is bigger than a certain number explicitly related to $r$ and $n$. As a consequence we deduce certain quantitative weighted estimates for bilinear homogeneous singular integrals associated with rough homogeneous kernels.
