Geodesic
Multi-linear operators given by singular multipliers
Muscalu, Camil1, 2 ; Tao, Terence3, 2 ; Thiele, Christoph2
1 Department of Mathematics, Brown University, Providence, Rhode Island 02912
2 Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
3 School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia
Journal of the American Mathematical Society, Tome 15 (2002) no. 2, pp. 469-496

Voir la notice de l'article provenant de la source American Mathematical Society

We prove $L^p$ estimates for a large class of multi-linear operators, which includes the multi-linear paraproducts studied by Coifman and Meyer (1991), as well as the bilinear Hilbert transform and other operators with large groups of modulation symmetries.
DOI : 10.1090/S0894-0347-01-00379-4

Muscalu, Camil 1, 2 ; Tao, Terence 3, 2 ; Thiele, Christoph 2

1 Department of Mathematics, Brown University, Providence, Rhode Island 02912
2 Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90095-1555
3 School of Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia 
@article{10_1090_S0894_0347_01_00379_4,
     author = {Muscalu, Camil and Tao, Terence and Thiele, Christoph},
     title = {Multi-linear operators given by singular multipliers},
     journal = {Journal of the American Mathematical Society},
     pages = {469--496},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2002},
     doi = {10.1090/S0894-0347-01-00379-4},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-01-00379-4/}
}
TY  - JOUR
AU  - Muscalu, Camil
AU  - Tao, Terence
AU  - Thiele, Christoph
TI  - Multi-linear operators given by singular multipliers
JO  - Journal of the American Mathematical Society
PY  - 2002
SP  - 469
EP  - 496
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-01-00379-4/
DO  - 10.1090/S0894-0347-01-00379-4
ID  - 10_1090_S0894_0347_01_00379_4
ER  - 
%0 Journal Article
%A Muscalu, Camil
%A Tao, Terence
%A Thiele, Christoph
%T Multi-linear operators given by singular multipliers
%J Journal of the American Mathematical Society
%D 2002
%P 469-496
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-01-00379-4/
%R 10.1090/S0894-0347-01-00379-4
%F 10_1090_S0894_0347_01_00379_4
Muscalu, Camil; Tao, Terence; Thiele, Christoph. Multi-linear operators given by singular multipliers. Journal of the American Mathematical Society, Tome 15 (2002) no. 2, pp. 469-496. doi: 10.1090/S0894-0347-01-00379-4

[1] Calderã³N, Calixto P. On commutators of singular integrals Studia Math. 1975 139 174

[2] Coifman, R. R., Meyer, Yves On commutators of singular integrals and bilinear singular integrals Trans. Amer. Math. Soc. 1975 315 331

[3] Coifman, R., Meyer, Y. Commutateurs d’intégrales singulières et opérateurs multilinéaires Ann. Inst. Fourier (Grenoble) 1978

[4] Coifman, R. R., Meyer, Y. Fourier analysis of multilinear convolutions, Calderón’s theorem, and analysis of Lipschitz curves 1980 104 122

[5] Coifman, Ronald R., Meyer, Yves Au delà des opérateurs pseudo-différentiels 1978

[6] Coifman, R. R., Meyer, Yves Nonlinear harmonic analysis, operator theory and P.D.E 1986 3 45

[7] Meyer, Yves, Coifman, R. R. Ondelettes et opérateurs. III 1991

[8] Fefferman, Charles Pointwise convergence of Fourier series Ann. of Math. (2) 1973 551 571

[9] Janson, Svante On interpolation of multilinear operators 1988 290 302

[10] Kenig, Carlos E., Stein, Elias M. Multilinear estimates and fractional integration Math. Res. Lett. 1999 1 15

[11] Lacey, Michael, Thiele, Christoph 𝐿^{𝑝} estimates on the bilinear Hilbert transform for 2<𝑝<∞ Ann. of Math. (2) 1997 693 724

[12] Lacey, Michael, Thiele, Christoph On Calderón’s conjecture Ann. of Math. (2) 1999 475 496

[13] Stein, Elias M. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals 1993

Cité par Sources :