## Lacey, Michael;Metcalfe, J.

*Paraproducts in One and Several Parameters*

ESI preprints (2005)### abstract

For multiparameter bilinear paraproduct operators $operatorname B$ we prove theestimate

begin{equation*}

operatorname Bmid L^ptimes L^q mapsto L^r, qquad 1

end{equation*}

Here, $1/p+1/q=1/r$ and special attention is paid to the case of $0<1$.

(Note that the families of multiparameter paraproducts are much richer than

in the one parameter case.)

These estimates are the essential step in the version of the multiparameter

Coifman-Meyer theorem proved by C.~Muscalu, J.~Pipher, T.~Tao, and C.~Thiele

cites{camil1,camil2}. We offer a different proof of these inequalities.

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