Mixed-norm estimates for paraproducts
Journées équations aux dérivées partielles (2016), Exposé no. 2, 10 p.

We present a new approach to the study of singular multi-parameter multilinear Fourier multipliers via multiple vector-valued inequalities. This summarizes some of our results from [1] and [2]. The main example is the bi-parameter paraproduct ΠΠ, for which we prove estimates within the whole range of admissible Lebesgue estimates.

Publié le :
DOI : 10.5802/jedp.643
Benea, Cristina 1 ; Muscalu, Camil 2

1 Laboratoire de Mathématiques Jean Leray Université de Nantes, UMR CNRS 6629 2, rue de la Houssinière 44322 Nantes Cedex 03, France
2 Department of Mathematics Cornell University Ithaca, NY 14853, USA
@article{JEDP_2016____A2_0,
     author = {Benea, Cristina and Muscalu, Camil},
     title = {Mixed-norm estimates for paraproducts},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     note = {talk:2},
     pages = {1--10},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2016},
     doi = {10.5802/jedp.643},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/jedp.643/}
}
TY  - JOUR
AU  - Benea, Cristina
AU  - Muscalu, Camil
TI  - Mixed-norm estimates for paraproducts
JO  - Journées équations aux dérivées partielles
N1  - talk:2
PY  - 2016
SP  - 1
EP  - 10
PB  - Groupement de recherche 2434 du CNRS
UR  - http://archive.numdam.org/articles/10.5802/jedp.643/
DO  - 10.5802/jedp.643
LA  - en
ID  - JEDP_2016____A2_0
ER  - 
%0 Journal Article
%A Benea, Cristina
%A Muscalu, Camil
%T Mixed-norm estimates for paraproducts
%J Journées équations aux dérivées partielles
%Z talk:2
%D 2016
%P 1-10
%I Groupement de recherche 2434 du CNRS
%U http://archive.numdam.org/articles/10.5802/jedp.643/
%R 10.5802/jedp.643
%G en
%F JEDP_2016____A2_0
Benea, Cristina; Muscalu, Camil. Mixed-norm estimates for paraproducts. Journées équations aux dérivées partielles (2016), Exposé no. 2, 10 p. doi : 10.5802/jedp.643. http://archive.numdam.org/articles/10.5802/jedp.643/

[1] Benea, Cristina; Muscalu, Camil Multiple Vector Valued Inequalities via the Helicoidal Method (2015) (http://arxiv.org/pdf/1511.04948v1.pdf)

[2] Benea, Cristina; Muscalu, Camil Quasi-Banach Valued Inequalities via the Helicoidal method (2016) (https://arxiv.org/pdf/1609.01090v1.pdf)

[3] Bernicot, Frédéric Local estimates and global continuities in Lebesgue spaces for bilinear operators, Anal. PDE, Volume 1 (2008) no. 1, pp. 1-27 | DOI | MR

[4] Carleson, Lennart On convergence and growth of partial sums of Fourier series, Acta. Math. (1966), pp. 135-157

[5] Coifman, R.; Meyer, Y. Wavelets, Calderón-Zygmund Operators and Multilinear Operators, Cambridge University Press, 1997

[6] Di Plinio, Francesco; Ou, Yumeng Banach-valued multilinear singular integrals (2015) (http://arxiv.org/abs/1506.05827, Online; accessed June 2016)

[7] Fefferman, Charles Pointwise convergence of Fourier Series, The Annals of Mathematics (1973), pp. 551-571

[8] Journé, Jean-Lin Calderón-Zygmund operators on product spaces, Revista Matemética Iberoamericana, Volume 1 (1985) no. 3, pp. 55-91 http://eudml.org/doc/39324

[9] Kenig, Carlos; Ponce, Gustavo; Vega, Luis Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle, Comm. Pure Appl. Math. (1993), pp. 527-620

[10] Lacey, Michael; Thiele, Christoph On Calderón’s conjecture, Ann. of Math. (2), Volume 149 (1999) no. 2, pp. 475-496 | DOI | MR

[11] Muscalu, Camil; Pipher, Jill; Tao, Terence; Thiele, Christoph Bi-parameter paraproducts, Acta Mathematica (2004), pp. 269-296

[12] Muscalu, Camil; Pipher, Jill; Tao, Terence; Thiele, Christoph Multi-parameter paraproducts, Rev. Mat. Iberoamericana (2006), pp. 963-976

[13] Muscalu, Camil; Schlag, Wilhem Classical and Multilinear Harmonic Analysis, Cambridge University Press, 2013

[14] Muscalu, Camil; Tao, Terence; Thiele, Christoph Multi-linear operators given by singular multipliers, J. Amer. Math. Soc. (2002), pp. 469-496

[15] Ruan, Zhuoping Multi-parameter Hardy spaces via discrete Littlewood-Paley theory, Anal. Theory Appl., Volume 26 (2010) no. 2, pp. 122-139

[16] Silva, Prabath Vector Valued Inequalities for Families of Bilinear Hilbert Transforms and Applications to Bi-parameter Problems, J. Lond. Math. Soc. (2014), pp. 695-724

Cité par Sources :