The Hörmander multiplier theorem for multilinear operators

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The Kato-Ponce Inequality (2013, methodology): “Lastly, we show that σ s fails to satisfy the condition given in [20] and also in [12] when s n .”
Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness (2014, methodology): “For further improvement in this direction in the case 0 < r ≤ 1 or the case where p or q can be smaller than or equal to 1, see the works in Grafakos, Miyachi and Tomita [14], Miyachi and Tomita [15] and Grafakos and Si [16].”
Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces (2017, methodology): “We are able to treat multipliers Tmν with limited amount of regularity by applying some of the tools introduced by Tomita [54], and further developed by Fujita– Tomita [32], Grafakos–Si [38], Grafakos–Miyachi–Tomita [36], Miyachi–Tomita [49], and Li–Sun [46] for ν = 0, and Chaffee–Torres–Wu [16] for”
On Multilinear Fourier Multipliers of Limited Smoothness (2013, unknown): “It is straightforward to verify that m satisfies condition (1.6) for |α1| + · · · + |αN | s but not for larger |α1| + · · · + |αN |, and thus the smoothness of m is “limited”.”
Minimal smoothness conditions for bilinear Fourier multipliers (2013, methodology): “In more recent papers [20], [9], and [8], results under much weaker assumptions are given, which we shall mention later.”