中文摘要：

为了证明双参数双线性的Coifman-Meyer乘子算子定理,一种二进双参数仿积∏（f,g）（x,y）=R∈RΣ1｜R｜1/2〈f,ΦR1〉,〈g,ΦR2〉ΦR3（x,y）被引入,其Lr有界性被证明,即‖∏（f,g）‖Lr茱‖f‖Lp‖f‖Lq,其中1/r=1/p＋1/q,q〈∞.但目前仍没有相应的加权有界性结果.利用对偶原理研究了∏（f,g）的加权有界性,即成立‖∏（f,g）‖Lr（ω）茱‖f‖Lp（ω）‖g‖Lp（ω）,其中1/r=1/p＋1/q,1〈p,q〈∞,ω∈Ar（R×R）.

英文摘要：

To prove bi-linear and bi-parameter Coifman-Meyer multiplier theorem, Mathematicians have introduced the following dyadic bi-parameter paraproduct1123∏（f, g）（x, y） =Σ1/2f, ΦR, g, ΦRΦR（x, y）R∈R R r and have proved its L boundedness, that is ‖∏（f, g）‖rL‖f‖pL‖f‖q, L where 1/r = 1/p ＋ 1/q, q ∞. But there is no any result of weighted estimates of the above paraproduct. In this paper, the weighted boundedness of ∏（ f, g）via duality was investigated. that is, ‖∏（ f, g）‖r L（ω）‖f‖p L（ω）‖g‖p L（ω）, where 1/r = 1/p ＋ 1/q, 1 p, q ∞,ω∈Ar（R × R）.