Lacey, Michael;Metcalfe, J.

Paraproducts in One and Several Parameters

ESI preprints (2005)

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abstract

For multiparameter bilinear paraproduct operators $operatorname B$ we prove the
estimate
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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