• 대한수학회보
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• 제59권5호
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• pp.1255-1268
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• 2022

We consider the Schrödinger type operator 𝓛 = (-𝚫_ℍⁿ)² + V² on the Heisenberg group ℍⁿ, where 𝚫_ℍⁿ is the sub-Laplacian and the non-negative potential V belongs to the reverse Hölder class RH_s for s ≥ Q/2 and Q ≥ 6. We shall establish the (L^p, L^q) estimates for the Riesz transforms T_𝛼,𝛽,j = V^2𝛼𝛁^j_ℍⁿ𝓛^-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.