Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE BOUNDEDNESS OF SOME BILINEAR SINGULAR INTEGRAL OPERATORS ON BESOV SPACES

  • Xu Ming (Institute of Mathematics Chinese Academy of Sciences)
  • Published : 2006.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we weaken the kernel conditions of bilinear Calderon-Zygmund operators and prove boundedness on Besov spaces.

Keywords

References

  1. R. Coifman and Y. Meyer,On commutators of singular integrals and bilinear sin- gular integrals, Trans. Amer. Math. Soc. 212 (1975), 315-331 https://doi.org/10.2307/1998628
  2. R. Coifman and Y. Meyer, Commutateurs d'integrales singuliµers et operateurs multiline aires, Ann. Inst. Fourier. Grenoble. 28 (1978), no. 3, xi, 177-202 https://doi.org/10.5802/aif.708
  3. R. Coifman and Y. Meyer, Au delµa des Operateurs pseudo-differentiels, Asterisque 57 (1978)
  4. G. David and J. L. Journe, A boundedness criterion for generalized Calderon- Zygmund operators, Ann. of Math. 120 (1984), no. 2, 371-397 https://doi.org/10.2307/2006946
  5. M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Func. Anal. 93 (1990), 34-170 https://doi.org/10.1016/0022-1236(90)90137-A
  6. L. Grafakos and R. H. Torres, On multilinear singular integrals of Caderon- Zygmund type, Publ. Mat. Vol. extra (2002), 57-91
  7. L. Grafakos and R. H. Torres, Multilinear singular integrals of Caderon-Zygmund theory, Advances. in Mathematics 165 (2002), 124-164 https://doi.org/10.1006/aima.2001.2028
  8. L. Grafakos and R. H. Torres, Discrete decompositions for bilinear operators and almost diagonal conditions, Trans. Amer. Math. Soc. 354 (2002), no. 3, 1153-1176 https://doi.org/10.1090/S0002-9947-01-02912-9
  9. L. Grafakos and R. H. Torres, Maximal operators and weighted norm inequalities for multilinear singular integrals, Indiana. Univ. Math. J. 51 (2002), no. 5, 1261-1276 https://doi.org/10.1512/iumj.2002.51.2114
  10. Y. S. Han, Inhomogeneous Calderon reproducing formula on spaces of homoge- neous type, J. Geom. Anal. 7 (1997), no. 2, 259-284 https://doi.org/10.1007/BF02921723
  11. Y. S. Han and S. Hofmann, T1 theorems for Besov and Triebel-Lizorkin spaces, Trans. Amer. Math. Soc. 337 (1993), 839-853 https://doi.org/10.2307/2154246
  12. Y. S. Han, S. Z. Lu, and D. C. Yang, Inhomogeneous Besov and Triebel-Lizorkinspaces on spaces of homogeneous type, Approx. Theory. Appl. 15 (1999), no. 3, 37-65
  13. M. Lacey and C. Thiele, $L^p$ estimates on the bilinear Hilbert transform, 2 < p < $\infty$, Ann. of Math. 146 (1997), no. 3, 693{724 https://doi.org/10.2307/2952458
  14. M. Lacey and C. Thiele, On Calderon's conjecture, Ann. of Math. 149 (1999), no. 2, 475-496 https://doi.org/10.2307/120971

Cited by

  1. The boundedness of bilinear singular integral operators on Sierpinski gaskets vol.27, pp.1, 2011, https://doi.org/10.1007/s10496-011-0092-9