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  • Bulletin of the Australian Mathematical Society, Volume 67, Issue 2
  • April 2003, pp. 187-200

Commutators of BMO functions and singular integral operators with non-smooth kernels

  • Xuan Thinh Duong (a1) and Lixin Yan (a2)
  • DOI: http://dx.doi.org/10.1017/S0004972700033669
  • Published online: 01 April 2009
Abstract

Let χ be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on Lp (χ) for some p, 1 < p < ∞. We give a sufficient condition on the kernel of T so that when a function b ∈ BMO(χ), the commutator [b, T](f) = T (bf) – bT (f) is bounded on Lp spaces for all p, 1 < p > ∞. Our condition is weaker than the usual Hörmander condition. Applications include Lp-boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrödinger operators, and divergence form operators on irregular domains.

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[5]R.R. Coifman , R. Rochberg and G. Weiss , ‘Factorization theorem for Hardy spaces in several variables’, Ann. of Math. 103 (1976), 611635.

[6]R.R. Coifman and G. Weiss , Analyse harmonique non-commutative sur certains espaces homognès, Lecture Notes in Math. 242 (Springer-Verlag, Berlin, Heidelberg, New York, 1971).

[10]S. Janson , ‘Mean oscillation and commutators of singular integrals operators’, Ark. Mat. 16 (1978), 263270.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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