East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON QUANTITATIVE TWO WEIGHT ESTIMATES FOR SOME DYADIC OPERATORS

  • Chung, Daewon (Faculty of Basic Sciences, Mathematics Major, Keimyung University)
  • Received : 2022.03.05
  • Accepted : 2022.04.20
  • Published : 2022.05.18
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Abstract

In this paper, a comparison of two types of quantitative two weight conditions for the boundedness of the dyadic paraproduct and the commutator of the Hilbert transform is provided. In the case of the commutator [b, H], the conditions of the well-known Bloom's inequality [2] and the slightly different types of two weight inequality introduced in [1] are compared around the A2-conditions on weights and the novel conditions on the function b.

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References

  1. O. Beznosova, D. Chung, J.C. Moraes, and M.C. Pereyra, On two weight estimates for dyadic operators, Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 2) AWM Series 5, Springer International Publishing (2017) 135-169
  2. S. Bloom, A commutator theorem and weighted BMO, Trans. Amer. Math. Soc. 292 (1985), no. 1, 103-122. https://doi.org/10.1090/S0002-9947-1985-0805955-5
  3. D. Chung, Sharp estimates for the commutators of the Hilbert, Riesz transforms and the Beurling-Ahlfors operator on weighted Lebsgue spaces, Indiana Univ. Math. Journal, 60 (2011) no. 5, 1543-1588. https://doi.org/10.1512/iumj.2011.60.4453
  4. D. Chung, On a two weights estimate for the commutator, East Asian Math. J. 33 (2017), no.1, 103-113. https://doi.org/10.7858/EAMJ.2017.010
  5. I. Holmes, M.T. Lacey and B.D. Wick, Blooms inequality: commutators in a two-weight setting, Arch. Math. 106 (2016), no. 1, 53-63. https://doi.org/10.1007/s00013-015-0840-8
  6. I. Holmes, M.T. Lacey and B.D. Wick, Commutators in the two-weight setting, Math. Ann. (2016). doi:10.1007/s00208-016-1378-1.
  7. T. Hytonen and A. Kairema, Systems of dyadic cubes in a doubling metric space, Colloq. Math. 126 (2012), 1-33. https://doi.org/10.4064/cm126-1-1
  8. J. C. Moraes, Weighted estimates for dyadic operators with complexity PhD Dissertation, University of New Mexico, (2011)
  9. J. C. Moraes and M.C. Pereyra, Weighted estimates for dyadic Paraproduct and t-Haar multiplies with complexity (m, n), Publ. Mat. 57 (2013), 265-294. https://doi.org/10.5565/PUBLMAT_57213_01
  10. F. Nazarov, S. Treil and A. Volberg, The Bellman functions and the two-weight inequalities for Haar Multipliers, Journal of the AMS, 12 (1992), 909-928.