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 $gammain (0,,1]$, $A$ has derivatives of order one in ${rm BMO}(mathbb{R}^n)$.