Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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WEIGHTED NORM ESTIMATES FOR THE DYADIC PARAPRODUCT WITH VMO FUNCTION

  • Chung, Daewon (Major in Mathematics Faculty of Basic Sciences Keimyung University)
  • Received : 2020.03.03
  • Accepted : 2020.08.21
  • Published : 2021.01.31
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Abstract

In [1], Beznosova proved that the bound on the norm of the dyadic paraproduct with b ∈ BMO in the weighted Lebesgue space L2(w) depends linearly on the Ad2 characteristic of the weight w and extrapolated the result to the Lp(w) case. In this paper, we provide the weighted norm estimates of the dyadic paraproduct πb with b ∈ VMO and reduce the dependence of the Ad2 characteristic to 1/2 by using the property that for b ∈ VMO its mean oscillations are vanishing in certain cases. Using this result we also reduce the quadratic bound for the commutators of the Calderón-Zygmund operator [b, T] to 3/2.

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References

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