“…, k − 1, and ∞. However, the corresponding analogs of Theorem 3 would involve operators of complexity similar as to the so-called multilinear and simplex Hilbert transforms (see [14], [19], [21]), for which no L p -boundedness results are known at the time of writing. An encouraging sign is that the papers [19] and [21] establish estimates for the truncations of these operators with constants o(J) in the number of consecutive dyadic scales J, while [6] improves this bound to J 1−ǫ for some ǫ > 0.…”