Abstract In this paper, we give a boundedness criterion for the potential operator ℐ α { {\mathcal I} }^{\alpha } in the local generalized Morrey space L M p , φ { t 0 } ( Γ ) L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the generalized Morrey space M p , φ ( Γ ) {M}_{p,\varphi }(\text{Γ}) defined on Carleson curves Γ \text{Γ} , respectively. For the operator ℐ α { {\mathcal I} }^{\alpha } , we establish necessary and sufficient conditions for the strong and weak Spanne-type boundedness on L M p , φ { t 0 } ( Γ ) L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the strong and weak Adams-type boundedness on M p , φ ( Γ ) {M}_{p,\varphi }(\text{Γ}) .

中文翻译：

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局部广义莫雷空间中卡尔森曲线上潜在算子的表征

摘要 在本文中，我们给出了局部广义莫雷空间 LM p 中的势算子 ℐ α { {\mathcal I} }^{\alpha } 的有界准则，φ { t 0 } ( Γ ) L{M}_ {p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) 和广义莫雷空间 M p , φ ( Γ ) {M}_{p,\varphi }( \text{Γ}) 分别定义在 Carleson 曲线 Γ \text{Γ} 上。对于算子 ℐ α { {\mathcal I} }^{\alpha } ，我们为 LM p 上的强和弱 Spane 型有界建立充分必要条件，φ { t 0 } ( Γ ) L{M}_ {p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) 和强弱 Adams 型有界在 M p , φ ( Γ ) {M}_{p ,\varphi }(\text{Γ}) 。