Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ESTIMATES FOR THE RIESZ TRANSFORMS ASSOCIATED WITH SCHRÖDINGER TYPE OPERATORS ON THE HEISENBERG GROUP

  • Wang, Yanhui (Department of Mathematics Jiaozuo University)
  • Received : 2021.09.24
  • Accepted : 2021.12.31
  • Published : 2022.09.30
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Abstract

We consider the Schrödinger type operator 𝓛 = (-𝚫ℍn)2 + V2 on the Heisenberg group ℍn, where 𝚫ℍn is the sub-Laplacian and the non-negative potential V belongs to the reverse Hölder class RHs for s ≥ Q/2 and Q ≥ 6. We shall establish the (Lp, Lq) estimates for the Riesz transforms T𝛼,𝛽,j = V2𝛼𝛁jℍn𝓛-𝛽, j = 0, 1, 2, 3, where 𝛁ℍn is the gradient operator on ℍn, 0 < α ≤ 1-j/4, j/4 < 𝛽 ≤ 1, and 𝛽 - 𝛼 ≥ j/4.

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References

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