Carleson Measures Associated with Families of Multilinear Operators
نویسندگان
چکیده
Abstract. In this work we investigate the construction of Carleson measures from families of multilinear integral operators applied to tuples of L∞ and BMO functions. We show that if the family Rt of multilinear operators possesses cancellation in each variable, then for BMO functions b1, . . . , bm, the measure |Rt(b1, . . . , bm)(x)|dxdt/t is Carleson. However, if the family of multilinear operators has cancellation in all variables combined this result is still valid if bj are L∞ functions, but it may fail if bj are unbounded BMO functions, as we indicate via an example. As an application of our results we obtain a multilinear quadratic T (1) type theorem and a multilinear version of a quadratic T (b) theorem analogous to those in Semmes [23].
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