Bellman function technique for multilinear estimates and an application to generalized paraproducts Vjekoslav Kovac 42B20paraproductmultilinear operatorBellman functioninteger partition We prove $\mathrm{L}^p$ estimates for a class of two-dimensional multilinear forms that naturally generalize (dyadic variants of) both classical paraproducts and the twisted paraproduct introduced in [C. Demeter and C. Thiele, \textit{On the two-dimensional bilinear Hilbert transform}, Amer. J. Math. \textbf{132} (2010), no. 1, 201--256] and studied in [F. Bernicot, \textit{Fiber-wise Calder\'on-Zygmund decomposition and application to a bi-dimensional paraproduct}, Illinois J. Math., to appear] and [V. Kova\{v}c, \textit{Boundedness of the twisted paraproduct}, Rev. Mat. Iberoam., to appear]. The method we use builds on the approach from [V. Kova\{v}c, \textit{Boundedness of the twisted paraproduct}, Rev. Mat. Iberoam., to appear], and we present it as a rather general technique for proving estimates on dyadic multilinear operators. In the particular application to "generalized paraproducts" this method is combined with combinatorics of integer partitions. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4784 10.1512/iumj.2011.60.4784 en Indiana Univ. Math. J. 60 (2011) 813 - 846 state-of-the-art mathematics http://iumj.org/access/