On the Hardy-Littlewood Maximal Operator in Zorko Spaces
Keywords:
maximal operator, Hardy-Littlewood, boundedness, closedness, Zorko spacesAbstract
Zorko spaces are introduced to address the density issue in Morrey spaces which are defined by utilizing the difference of a function of first order. Later the difference of a function of second order is also employed to define modified Zorko spaces and approximation properties are investigated therein. On the other hand, integral operators are mostly studied on the boundedness properties in Morrey spaces and its variants. In this paper, integral operators, especially Hardy-Littlewood maximal operators and fractional Hardy-Littlewood maximal operators, are investigated its boundedness and closedness properties in Zorko spaces.
References
Adams, D. R. (2015). Morrey spaces (J. J. Benedettoo, Ed.). Springer International Publishing.
Adams, D. R., & Xiao, J. (2004). Nonlinear potential analysis on Morrey spaces and their capacities. Indiana University Mathematics Journal, 53(6), 1631–1666. https://doi.org/10.1512/iumj.2004.53.2470
Adams, D. R., & Xiao, J. (2012). Morrey spaces in harmonic analysis. Arkiv for Matematik, 50(2), 201–230. https://doi.org/10.1007/s11512-010-0134-0
Chiarenza, F., & Frasca, M. (1987). Morrey spaces and Hardy-Littlewood maximal function. Rend. Mat. Apple. (7), 7, 273–279.
Deringoz, F. (2024). Hardy–Littlewood maximal operator in a new vanishing Orlicz–Morrey space. Zeitschrift Für Analysis Und Ihre Anwendungen. https://doi.org/10.4171/zaa/1778
Diarra, N., & Fofana, I. (2023). Characterization of some closed linear subspaces of Morrey spaces and approximation. Advances in Pure and Applied Mathematics, 14(3), 41–72. https://doi.org/10.21494/ISTE.OP.2023.0980
Gogatishvili, A., & Mustafayev, R. Ch. (2015). A note on boundedness of the Hardy-Littlewood maximal operator on Morrey spaces. Mediterranean Journal of Mathematics, 13(4), 1885–1891. https://doi.org/10.1007/s00009-015-0614-3
Gunawan, H., & Schwanke, C. (2019). The Hardy–Littlewood maximal operator on discrete morrey spaces. Mediterranean Journal of Mathematics, 16(1). https://doi.org/10.1007/s00009-018-1277-7
Hao, X. B., Li, B. D., & Yang, S. (2024). The Hardy–Littlewood maximal operator on discrete weighted Morrey spaces. Acta Mathematica Hungarica, 172(2), 445–469. https://doi.org/10.1007/s10474-024-01420-3
Hasanah, D., & Gunawan, H. (2024). Approximation in modified Zorko spaces. Analysis Mathematica, 50(2), 553–561. https://doi.org/10.1007/S10476-024-00025-W/METRICS
Hasanah, D., & Gunawan, H. (2025). Approximation in generalized Morrey spaces using the second-order difference. Mathematical Inequalities & Applications, 28(1), 159–172. https://doi.org/10.7153/mia-2025-28-11
Ho, K.-P. (2013). The fractional integral operators on Morrey spaces with variable exponent on unbounded domains. Mathematical Inequalities & Applications, (2), 363–373. https://doi.org/10.7153/mia-16-27
Morrey, C. B. (1938). On the solutions of quasi-linear elliptic partial differential equations. Transactions of the American Mathematical Society, 43(1), 126. https://doi.org/10.2307/1989904
Nekvinda, A. (2004). Hardy-Littlewood maximal operator on L^p(x)(R). Mathematical Inequalities & Applications, 7(2), 255–265.
Ramadana, Y., & Gunawan, H. (2023). Boundedness of the Hardy–Littlewood maximal operator, fractional integral operators, and calderón–zygmund operators on generalized weighted morrey spaces. Khayyam Journal of Mathematics, 9(2), 263–287. https://doi.org/10.22034/KJM.2023.386608.2779
Zhou, J., & Zhao, F. (2022). Boundedness of the fractional Hardy-Littlewood maximal operator on weighted Morrey spaces. Analysis and Mathematical Physics, 12(4), 87. https://doi.org/10.1007/s13324-022-00695-5
Zorko, C. T. (1986). Morrey space. Proceedings of the American Mathematical Society, 98(4), 586–592.
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