一类多线性奇异积分算子的加权估计

In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by TAf(x) = p. v.RnΩ(x- y)|x- y|n+1 A(x)- A(y)- A(y)(x- y) f(y)dy,where Ω is homogeneous of degree zero, has vanishing moment of order one, and belongs to Lipγ(Sn-1) with γ∈(0, 1], A has derivatives of order one in BMO(Rn).

Weighted Norm Inequalities for a Class of Multilinear Singular Integral Operators

In this paper, weighted estimates with general weights are established for the multilinear singular integral operator defined by $$T_{A}f(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)(x-y)\big)f(y)\d y,$$ where $\Omega$ is homogeneous of degree zero, has vanishing moment of order one, and belongs to ${\rm Lip}_{\gamma}(S^{n-1})$ with $\gamma\in (0,\,1]$, $A$ has derivatives of order one in ${\rm BMO}(\mathbb{R}^n)$.