Abstract In this paper, the necessary and sufficient conditions are found for the boundedness of the Riesz potential I α {I_{\alpha}} in the local Morrey–Lorentz spaces M p , q ; λ loc ⁢ ( ℝ n ) {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})} . This result is applied to the boundedness of particular operators such as the fractional maximal operator, fractional Marcinkiewicz operator and fractional powers of some analytic semigroups on the local Morrey–Lorentz spaces M p , q ; λ loc ⁢ ( ℝ n ) {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})} .

中文翻译：

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局部 Morrey-Lorentz 空间中的 Riesz 势和一些应用

摘要 本文找到了局部 Morrey-Lorentz 空间 M p , q 中 Riesz 势 I α {I_{\alpha}} 有界的充要条件；λ loc ⁢ ( ℝ n ) {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})} 。该结果适用于特定算子的有界性，例如分数极大算子、分数 Marcinkiewicz 算子和局部 Morrey-Lorentz 空间 M p , q 上一些解析半群的分数幂；λ loc ⁢ ( ℝ n ) {M_{p,q;{\lambda}}^{\mathrm{loc}}({\mathbb{R}^{n}})} 。