Geodesic
Lp estimates for multi-linear and multi-parameter pseudo-differential operators
[Estimations Lp pour les opérateurs pseudo-différentiels multilinéaires et multiparamètres]
Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 3, pp. 567-597

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We establish the pseudo-differential variant of the Lp estimates for multi-linear and multi-parameter Coifman-Meyer multiplier operators proved by C. Muscalu, J. Pipher, T. Tao and C. Thiele in [21, 22]. This gives an affirmative answer to the question, raised in the book of C. Muscalu and W. Schlag [23], on whether the Lp estimates for multi-linear and multi-parameter pseudo-differential operators hold.

Publié le :
DOI : 10.24033/bsmf.2698
Classification : 35S05, 42B15, 42B20
Keywords: Multi-linear and multi-parameter pseudo-differential operators, One-parameter and multi-parameter paraproducts, $L^{p}$ estimates, Coifman-Meyer theorem. 
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     author = {Dai, Wei and Lu, Guozhen},
     title = {$L^{p}$ estimates for multi-linear and multi-parameter pseudo-differential operators},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {567--597},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {143},
     number = {3},
     year = {2015},
     doi = {10.24033/bsmf.2698},
     mrnumber = {3417733},
     zbl = {1335.47033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2698/}
}
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Dai, Wei; Lu, Guozhen. $L^{p}$ estimates for multi-linear and multi-parameter pseudo-differential operators. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 3, pp. 567-597. doi: 10.24033/bsmf.2698

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