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SOME BILINEAR ESTIMATES
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 Title & Authors
SOME BILINEAR ESTIMATES
Chen, Jiecheng; Fan, Dashan;
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 Abstract
We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.
 Keywords
Hilbert transform;fractional integral;bilinear operators;Sobolev spaces;
 Language
English
 Cited by
1.
Bilinear Calderón-Zygmund operators of type ω(t) on non-homogeneous space, Journal of Inequalities and Applications, 2014, 2014, 1, 113  crossref(new windwow)
2.
Rough bilinear fractional integrals with variable kernels, Frontiers of Mathematics in China, 2010, 5, 3, 369  crossref(new windwow)
 References
1.
A. Benyi, A. Nahmod, and R. H. Torres, Sobolev space estimates and symbolic calculus for bilinear pseudodifferential operators, J. Geom. Anal. 16 (2006), no. 3, 431–453 crossref(new window)

2.
A. Benyi, C. Demeter, A. Nahmod, C. Thiele, R. H. Torres, and P. Villaroya, Modulation invariant bilinear T(1) theorem, on the ArXiv

3.
M. Cowling, A. M. Mantero, and F. Ricci, Pointwise estimates for some kernels on compact Lie groups, Rend. Circ. Mat. Palermo (2) 31 (1982), no. 2, 145–158 crossref(new window)

4.
Y. Ding and C. Lin, Rough bilinear fractional integrals, Math. Nachr. 246/247 (2002), 47–52 crossref(new window)

5.
D. Fan and S. Sato, Transference on certain multilinear multiplier operators, J. Aust. Math. Soc. 70 (2001), no. 1, 37–55 crossref(new window)

6.
J. Gilbert and A. Nahmod, Boundedness of bilinear operators with nonsmooth symbols, Math. Res. Lett. 7 (2000), no. 5-6, 767–778

7.
L. Grafakos and N. Kalton, Some remarks on multilinear maps and interpolation, Math. Ann. 319 (2001), no. 1, 151–180 crossref(new window)

8.
I. Hirschman, On multiplier transformations, Duke Math. J. 26 (1959), 221–242

9.
S. Janson, On interpolation of multilinear operators, Function spaces and applications (Lund, 1986), 290–302, Lecture Notes in Math., 1302, Springer, Berlin, 1988 crossref(new window)

10.
M. Kaneko, Boundedness of some operators composed of Fourier multipliers, Tohoku Math. J. (2) 35 (1983), no. 2, 267–288

11.
M. Kaneko, Boundedness of some operators composed of Fourier multipliers, Tohoku Math. J. (2) 35 (1983), no. 2, 267–288

12.
C. Kenig and E. Stein, Multilinear estimates and fractional integration, Math. Res. Lett. 6 (1999), no. 1, 1–15

13.
M. Lacey and C. Thiele, $L^p$ estimates on the bilinear Hilbert transform for $2, Ann. of Math. (2) 146 (1997), no. 3, 693–724

14.
K. de Leeuw, On Lp multipliers Ann. of Math. (2) 81 (1965), 364–379

15.
C. Muscalu, T. Tao, and C. Thiele, Multi-linear operators given by singular multipliers, J. Amer. Math. Soc. 15 (2002), no. 2, 469–496 crossref(new window)

16.
E. M. Stein, Topic in Harmonic Analysis, Ann. of Math. Studies 63, Princeton University Press, 1970

17.
C. Thiele, Multilinear singular integrals, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial, 2000). Publ. Mat. 2002, Vol. Extra, 229–274