Abstract. Weighted analogues of de Leeuw's restriction theorem for Fourier multipliers on L p (R n ) are obtained. Weighted analogues of related extension theorems for multipliers on L p (T) are also considered.
In this paper we have obtained the boundedness of bilinear Littlewood-Paley operators on the circle group T by using appropriate transference techniques. In particular, bilinear analogue of Carleson's Littlewood-Paley result for all possible indices has been obtained. Also, we prove some bilinear analogues of de Leeuw's results concerning multipliers of R n .
In this paper we prove the bilinear analogue of de Leeuw's result for periodic bilinear multipliers and some Jodeit type extension results for bilinear multipliers.
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