A Weighted Weak Type Endpoint Estimate for the Multilinear Calder\'on-Zygmund Operators and Its Applications
Received:November 23, 2007  Revised:May 21, 2008
Key Word: multilinear Calder\'on-Zygmund operator   maximal operator   weighted norm inequality   interpolation.
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10671210).
 Author Name Affiliation Guo Qiang PENG Department of Applied Mathematics, Information Engineering University, Henan 450002, P. R. China
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A weighted weak type endpoint estimate is established for the $m$-linear operator with Calder\'on-Zygmund kernel, which was introduced by Coifman and Meyer. As applications, the mapping properties on weighted $L^{p_1}(\rn)\times\cdots\times L^{p_m}(\rn)$ with weight $M_Bw$ for certain maximal operator $M_B$ and general weight $w$, and a two-weight weighted norm estimate for this operator, are obtained.