Multi-parameter paraproducts

By Camil Muscalu, Jill Pipher, Terence Tao, C. Thiele. 2004

123 citations recorded by the source corpus.

We prove that classical Coifman-Meyer theorem holds on any polidisc Td or arbitrary dimension d = 1

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fb093359d7b0c35ae30997416b8999cd35e241e4

How researchers see this paper

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In Applied Mathematics

1. G. Lu
2. Jiao Chen
3. Robert M. Strain
4. Yan Guo
5. C. Benea
6. Philip T. Gressman
7. Akihiko Miyachi
8. Benoit Pausader

In Computational Theory and Mathematics

1. C. Benea
2. G. Lu
3. Jiao Chen
4. Benoit Pausader
5. Yan Guo
6. Camil Muscalu
7. Naohito Tomita
8. Jill Pipher

In Mathematical Physics

1. G. Lu
2. Jiao Chen
3. Robert M. Strain
4. C. Benea
5. Yan Guo
6. Akihiko Miyachi
7. Benoit Pausader
8. Naohito Tomita

Citations in the corpus

• Global Smooth Ion Dynamics in the Euler-Poisson System (2010, methodology): “In particular, we cannot use the traditional Coifman-Meyer multiplier theorem [2], or a more refined version as in Muscalu, Pipher, Tao and Thiele [18, 19] since in all these cases, the multiplier need to satisfy some homogeneity conditions.”
• Minimal smoothness conditions for bilinear Fourier multipliers (2013, background): “For other results on these operators and related topics, see Muscalu–Pipher–Tao–Thiele [17], Bernicot–Germain [1], and the references therein.”
• Quasi-Banach Valued Inequalities via the Helicoidal method (2016, unknown): “ches invoke vector-valued inequalities in the study of multi-parameter multilinear operators. These operators are intriguing because they don’t always behave as expected. For example, in [MPTT04] and [MPTT06] it was shown that Π⊗Π is bounded, but BHT⊗BHTdoesn’t satisfy any Lp estimates of H¨older ty”
• Multiple Vector Valued Inequalities via the Helicoidal Method (2015, methodology): “Through our methods, we can also recover the results from [Muscalu et al. 2006a], stating that .”
• Hörmander type theorems for multi-linear and multi-parameter Fourier multiplier operators with limited smoothness (2014, methodology): “This theorem was extended to the case of multi-linear and multi-parameter setting in [19].”
• Multiparameter Riesz commutators (2007, background): “For a cone in C ⊂ R d , we fix a Calder´on–Zygmund kernel K C which satisfies the size and smoothness assumptions above, and in addition, Moreover, we choose the cone operator to make a sufficiently smooth transition from 0 to 1 that the operator T with symbol given by K defines a Calder´on– Zygmund…”
• Global classical solutions of the Boltzmann equation without angular cut-off (2009, background): “The operator and its associated trilinear form may be expressed in terms of Fourier transforms as a trilinear paraproduct; such objects have been the subject of recent work of Muscalu, Pipher, Tao, and Thiele [43] and are known to be very difficult to study in general.”