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January 2020 Characterizations for the fractional maximal operators on Carleson curves in local generalized Morrey spaces
Hatice Armutcu, Ahmet Eroglu, Fatai Isayev
Tbilisi Math. J. 13(1): 23-38 (January 2020). DOI: 10.32513/tbilisi/1585015217

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

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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

Information

Received: 16 September 2019; Accepted: 16 December 2019; Published: January 2020
First available in Project Euclid: 24 March 2020

zbMATH: 07200149
MathSciNet: MR4079447
Digital Object Identifier: 10.32513/tbilisi/1585015217

Subjects:
Primary: 42B20
Secondary: 42B25, 42B35

Rights: Copyright © 2020 Tbilisi Centre for Mathematical Sciences

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Vol.13 • No. 1 • January 2020
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