Bulletin of the Korean Mathematical Society (대한수학회보)

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TWO-WEIGHT NORM ESTIMATES FOR SQUARE FUNCTIONS ASSOCIATED TO FRACTIONAL SCHRÖDINGER OPERATORS WITH HARDY POTENTIAL

  • Tongxin Kang (School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University) ;
  • Yang Zou (School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University)
  • Received : 2022.10.29
  • Accepted : 2023.04.21
  • Published : 2023.11.30
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Abstract

Let d ∈ ℕ and α ∈ (0, min{2, d}). For any a ∈ [a*, ∞), the fractional Schrödinger operator 𝓛a is defined by 𝓛a := (-Δ)α/2 + a|x|-α, where $a^*:={\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}(d-{\alpha})/4)^2}}$. In this paper, we study two-weight Sobolev inequalities associated with 𝓛a and two-weight norm estimates for several square functions associated with 𝓛a.

Keywords

Acknowledgement

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 11871254 and 12071431), the Key Project of Gansu Provincial National Science Foundation (Grant No. 23JRRA1022), the Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2021-ey18) an

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