A Hörmander type multiplier theorem for multilinear operators

By Naohito Tomita. 2010

136 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/afac00fa1a70484a210e799079d5ae35064afe9b

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces (2017, methodology): “[54] N. Tomita, A Hörmander type multiplier theorem for multilinear operators, J. Func.”
The Hörmander multiplier theorem for multilinear operators (2012, result): “[15] N. Tomita, A Hörmander type multiplier theorem for multilinear operators, Jour.”
Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators (2019, background): “We refer the interested reader to [16, 35, 50] and references therein for more on background and related results.”
Sparse Domination Theorem for Multilinear Singular Integral Operators with $L^{r}$-Hörmander Condition (2016, background): “However, for the multilinear Hörmander condition ([11]), i.”
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): “To state the result in [13], form ∈ L∞(R2n), we setmk(ξ , η) = m(2kξ, 2kη)Ψ (ξ1, η1), where Ψ is the same as the (1.”
On Multilinear Fourier Multipliers of Limited Smoothness (2013, unknown): “In fact, Tomita [21] recently proved that if m ∈ L∞(RNn) satisfies sup j∈Z ‖mj‖W s(RNn) <∞ with s > Nn/2, then Tm is bounded from L1(R)×· · ·×LN (R) to L(R) for all 1 < p1, .”
Weighted norm inequalities for multilinear Fourier multipliers (2012, methodology): “In [17], the second author gave a Hörmander type theorem for multilinear Fourier multipliers.”
Minimal smoothness conditions for bilinear Fourier multipliers (2013, background): “Now, for bilinear Fourier multiplier operators, Grafakos–Miyachi–Tomita [8] have obtained some results with minimal conditions by using the product type Sobolev norms.”