多线性Fourier乘子算子的加权估计

Weighted norm inequalities for the multilinear Fourier multiplier operators

本文考虑多线性Fourier乘子算子在加权Lebesgue空间的乘积空间上的性质,利用多线性Fourier乘子算子的核估计以及多线性奇异积分算子的加权理论,建立多线性Fourier乘子算子的(关于多重Ap/r(Rmn)权函数以及关于一般权函数的)两个加权估计.

In this paper, the behavior on product of weighted Lebesgue spaces is considered for the multilin- ear Fourier multiplier operators. By the kernel estimates of the multilinear Fourier multiple operator and the weighted theory for the multilinear singular integral operators, two weighted norm inequalities （with respect to general weights and multiple Ap/t（R^mn） weights respectively） for the multilinear Fourier multiplier operators, are established.