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Higher order commutators for vector-valued Calderón-Zygmund operators


Authors: Carlos Segovia and José L. Torrea
Journal: Trans. Amer. Math. Soc. 336 (1993), 537-556
MSC: Primary 42B20; Secondary 42B25
DOI: https://doi.org/10.1090/S0002-9947-1993-1074151-6
MathSciNet review: 1074151
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Abstract: Weighted norm estimates for higher order commutators are obtained. The proof, that remain valid in the vector-valued case, are obtained as an application of some extrapolation results. The vector-valued version of the commutator theorem is applied to the Carleson operator, U.M.D. Banach spaces, approximate identities and maximal operators.


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  • [B] S. Bloom, A commutator theorem and weighted $ {\text{BMO}}$, Trans. Amer. Math. Soc. 292 (1985), 103-122. MR 805955 (87g:42021)
  • [Bu] D. L. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, Conference on Harmonic Analysis in Honor of Antoni Zygmund, University of Chicago, 1981, Wadsworth, Belmont, Calif., 1983. MR 730072 (85i:42020)
  • [CH] S. Chanillo, A note on commutators, Indiana Univ. Math. J. 31 (1982), 7-16. MR 642611 (84j:42027)
  • [CRW] R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces of several variables, Ann. of Math. (2) 103 (1976). MR 0412721 (54:843)
  • [CF] A. Córdoba and C. Fefferman, A weighted norm inequality for singular integrals, Studia Math. 57 (1976), 97-101. MR 0420115 (54:8132)
  • [RFC] J. García-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related topics, Math. Studies 116, North-Holland, Amsterdam, 1985. MR 848136 (87b:00011)
  • [HMS] E. Harboure, R. A. Macías and C. Segovia, Extrapolation results for classes of weights, Amer. J. Math. 110 (1988), 383-397. MR 944321 (89i:47055)
  • [H] R. A. Hunt, On the convergence of Fourier series, orthogonal expansions and their continuous analogues, Proc. Conf. Edwardsville, Southern Illinois Univ. Press, 1968, pp. 235-255. MR 0238019 (38:6296)
  • [KW] D. S. Kurtz and R. L. Wheeden, Results of weighted norm inequalities for multipliers, Trans. Amer. Math. Soc. 255 (1979), 343-362. MR 542885 (81j:42021)
  • [Mu] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226. MR 0293384 (45:2461)
  • [FRT] J. L. Rubio de Francia, F. J. Ruiz and J. L. Torrea, Calderón-Zygmund theory for operator-valued kernels, Adv. in Math. 62 (1986), 7-48. MR 859252 (88f:42035)
  • [RT] F. J. Ruiz and J. L. Torrea, Weighted and vector valued inequalities for potential operators, Trans. Amer. Math. Soc. 295 (1986), 213-232. MR 831197 (87g:42031)
  • [STa] C. Segovia and J. L. Torrea, Extrapolation of pairs of related weights, Analysis and Partial Differential Equations: A Collection of Papers Dedicated to Misha Cotlar, Marcel Dekker, New York, 1990. MR 1044797 (91e:42022)
  • [STb] -, Vector valued commutators and applications, Indiana Univ. Math. J. 38 (1989), 959-971. MR 1029684 (90k:47067)
  • [STW] J.-O. Strömberg and R. L. Wheeden, Fractional integral on weighted $ {H^p}$ and $ {L^p}$ spaces, Trans. Amer. Math. Soc. 287 (1985), 293-321. MR 766221 (86f:42016)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1074151-6
Article copyright: © Copyright 1993 American Mathematical Society

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