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Characterizations for the fractional maximal operators on Carleson curves in local generalized Morrey spaces. (English) Zbl 1439.42025

Summary: In this paper we study the fractional maximal operator \(\mathcal{M}^{\alpha}\) in the local generalized Morrey space \(LM_{p,\varphi}^{\{t_0\}}(\Gamma)\) and the generalized Morrey space \(M_{p,\varphi}(\Gamma)\) defined on Carleson curves \(\Gamma \), respectively. For the operator \(\mathcal{M}^{\alpha}\) we shall give a characterization the strong and weak Spanne-Guliyev type boundedness on \(LM_{p,\varphi}^{\{t_0\}}(\Gamma)\) and the strong and weak Adams-Guliyev type boundedness on \(M_{p,\varphi}(\Gamma)\).

MSC:

42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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References:

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