## 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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