• 대한수학회보
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• 제60권6호
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• pp.1567-1605
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• 2023

Let d ∈ ℕ and α ∈ (0, min{2, d}). For any a ∈ [a^*, ∞), the fractional Schrödinger operator 𝓛_a is defined by 𝓛_a := (-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 𝓛_a and two-weight norm estimates for several square functions associated with 𝓛_a.

• 대한수학회지
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• 제59권1호
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• pp.129-150
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• 2022

Let L = -∆ + V be a Schrödinger operator, where the potential V belongs to the reverse Hölder class. In this paper, by the subordinative formula, we investigate the generalized Poisson operator P^L_t,σ, 0 < σ < 1, associated with L. We estimate the gradient and the time-fractional derivatives of the kernel of P^L_t,σ, respectively. As an application, we establish a Carleson measure characterization of the Campanato type space 𝒞^𝛄_L (ℝⁿ) via P^L_t,σ.