Analogues of multi-parameter multiplier operators on are defined on the torus . It is shown that these operators satisfy the classical Coifman-Meyer theorem. In addition, end-point estimates are proved.
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John T. Workman, End-point estimates and multi-parameter paraproducts on higher dimensional tori. Rev. Mat. Iberoam. 26 (2010), no. 2, pp. 591–610DOI 10.4171/RMI/610