Abstract
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}})} .
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