East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

NOTES ON SAWYER TYPE ESTIMATES FOR THE DYADIC PARAPRODUCT

  • Daewon Chung (Faculty of Basic Sciences, Mathematics Major, Keimyung University)
  • Received : 2023.04.13
  • Accepted : 2023.05.28
  • Published : 2023.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we provide Sawyer type conditions on a pair of weights so that the dyadic paraproduct πb is bounded from L2(u) into L2(v). The conditions can be obtained by checking the boundedness of the dyadic paraproduct on a collection of test functions.

Keywords

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. J. Bony, Calcul symbolique et propagation des singularites pour les equations aux derives non-lineaires Ann. Sci. Ecole Norm. Sup., 14 (1981) 209-246. https://doi.org/10.24033/asens.1404
  3. G. David, J. abd L. Journe, A boundedness criterion for generalized Calderon-Zygmund operators, Ann. of Math., 20 (1984) 371-397.
  4. M. Lacey, Two Weight Inequality for the Hilbert Transform: A real variable characterization, II, Duke Math. J. 163 No. 15 (2014) 2821-2840.
  5. M. Lacey and K. Li, Two weight norm inequalities for the g function. Math. Res. Lett. 21 No. 3 (2014) 521-536. https://doi.org/10.4310/MRL.2014.v21.n3.a9
  6. M. Lacey, E. Sawyer, C.-Y. Shen and I. Uriarte-Tuero, The two weight inequality for the Hilbert transform, coronas and energy conditions, Duke Math. J. 163 No. 15 (2014) 2794-2820.
  7. F. Nazarov, S. Treil and A. Volberg, The Bellman functions and the two-weight inequalities for Haar Multipliers. Journal of the AMS, 12 (1999), 909-928.
  8. F. Nazarov, S. Treil and A. Volberg, Two weight inequalities for individual Haar multipliers and other well localized operators, Math. Res. Lett. 15 (2008), no. 3, 583-597. https://doi.org/10.4310/MRL.2008.v15.n3.a16
  9. M.C. Pereyra, Lecture notes on dyadic harmonic analysis. Contemporary Mathematics, 289 (2001) 1-60. https://doi.org/10.1090/conm/289/04874
  10. E. Sawyer, A characterization of a two weight norm inequality for maximal functions, Studia Math. 72 (1982), No. 1, 1-11. https://doi.org/10.4064/sm-75-1-1-11
  11. E. Sawyer, A characterization of two weight norm inequalities for fractional and Poisson integrals, Trans. Amer. Math. Soc. 308 (1988), No. 2, 533-545. https://doi.org/10.1090/S0002-9947-1988-0930072-6
  12. M. Wilson, Weighted inequalitites for the dyadic square function without dyadic A∞, Duke Math. J. 55 No. 1, (1987) 19-49.