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Some bilinear estimates

Dashan Fan|Jiecheng Chen
대한수학회 (The Korean Mathematical Society)|2009.05|대한수학회지 (Journal of the KMS)|제46권 제3호|pp. 609-620

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참고문헌

키워드

fractional integralHilbert transformSobolev spacesbilinear operators
주제분류수학

초록

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.

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.

참고문헌 (17)

  1. A. Nahmod, "Sobolev space estimates and symbolic calculus for bilinear pseudodifferential operators", J. Geom. Anal.., 16(3), pp.431~453 (2006)
  2. ´A. B´enyi, , Modulation invariant bilinear T(1) theorem, on the ArXiv, ~
  3. M. Cowling, "Pointwise estimates for some kernels on compact Lie groups", Rend. Circ. Mat. Palermo, 31(2), pp.145~158 (1982)
  4. Y. Ding, "Rough bilinear fractional integrals", Math. Nachr., 246, pp.47~52 (2002)
  5. D. Fan, "Transference on certain multilinear multiplier operators", J. Aust. Math. Soc., 70(1), pp.37~55 (2001)
  6. J. Gilbert, "Boundedness of bilinear operators with nonsmooth symbols", Math. Res. Lett., 7(5), pp.767~778 (2000)
  7. L. Grafakos, "Some remarks on multilinear maps and interpolation", Math. Ann., 319(1), pp.151~180 (2001)
  8. I. Hirschman, "On multiplier transformations", Duke Math. J., 26, pp.221~242 (1959)
  9. S. Janson, "On interpolation of multilinear operators, Function spaces and applications", pp.290~302 (1988), Lecture Notes in Math.
  10. M. Kaneko, "Boundedness of some operators composed of Fourier multipliers", Tohoku Math. J., 35(2), pp.267~288 (1983)
  11. T. Kato, "Commutator estimates and the Euler and Navier-Stokes equations", Comm. Pure Appl. Math., 41(7), pp.891~907 (1988)
  12. C. Kenig, "Multilinear estimates and fractional integration", Math. Res. Lett., 6(1), pp.1~15 (1999)
  13. M. Lacey, "Lp estimates on the bilinear Hilbert transform for 2 < p < 1", Ann. of Math., 146(3), pp.693~724 (1997)
  14. K. de Leeuw, "On Lp multipliers", Ann. of Math., 81, pp.364~379 (1965)
  15. C. Muscalu, "Multi-linear operators given by singular multipliers", J. Amer. Math. Soc., 15(2), pp.469~496 (2002)
  16. E. M. Stein, "Topic in Harmonic Analysis", Ann. of Math. Studies, 63 (1970), Princeton University Press
  17. C. Thiele, "Multilinear singular integrals, Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations", Publ. Mat., pp.229~274 (2002)

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