ar X iv : 0 81 1 . 28 54 v 1 [ m at h . FA ] 1 8 N ov 2 00 8 L p estimates for non smooth bilinear Littlewood - Paley square functions
نویسنده
چکیده
L p estimates for non smooth bilinear Littlewood-Paley square functions on R. Abstract In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. Mainly we prove boundedness-properties in Lebesgue spaces for them. Let us consider the function φn satisfying c φn(ξ) = 1 [n,n+1] (ξ) and consider the bilinear operator Sn(f, g)(x) := R f (x + y)g(x − y)φn(y)dy. These bilinear operators are closely related to the bilinear Hilbert transforms.
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