Abstract
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 $M_{p,\varphi}(\Gamma)$.
Funding Statement
The authors thank the referees for careful reading the paper and useful comments.
Citation
Hatice Armutcu. Ahmet Eroglu. Fatai Isayev. "Characterizations for the fractional maximal operators on Carleson curves in local generalized Morrey spaces." Tbilisi Math. J. 13 (1) 23 - 38, January 2020. https://doi.org/10.32513/tbilisi/1585015217
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