CHARACTERIZING THE COMPACTNESS OF CALDERÓN-ZYGMUND COMMUTATORS OF TYPE THETA ON GENERALIZED MORREY-LORENTZ SPACES
Main Article Content
Abstract
In this paper, we characterize the compactness of the Calderón-Zygmund commutator of type on generalized Morrey-Lorentz spaces . More precisely, we prove that if , which is the closure of , then is a compact operator on for all and .
Keywords
Calderón-Zygmund commutator of type, generalized Morrey-Lorentz space, compactness
Article Details
References
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Uchiyama, A. (1978). On the compactness of operators of Hankel type. Tohoku Mathematical Journal, Second Series, 30(1), 163-171. https://doi.org/10.2748/tmj/1178230105
Yabuta, K. (1985). Calderón-Zygmund operators and pseudo-differential operators. Communications in Partial Differential Equations, 10(9), 1005-1022. https://doi.org/10.1007/BFb0061458
Chen, Y., Ding, Y., & Wang, X. (2011). Compactness of Commutators for Singular Integrals on Morrey Spaces. Canadian Journal of Mathematics, 64(2),
257-281. https://doi.org/10.4153/cjm-2011-043-1
Dao, N. A., & Krantz, S. G. (2021). Lorentz boundedness and compactness characterization of integral commutators on spaces of homogeneous type. Nonlinear Analysis, 203,
Article 112162. https://doi.org/10.1016/j.na.2020.112162
Grafakos, L. (2008). Classical Fourier analysis (Vol. 2). Springer.
Le, T. N., Phan, T. P., Le, M. T., Du, K. T., & Tran, T. D. (2024). Calderón – Zygmund commutators of type theta on generalized Morrey – Lorentz space. Ho Chi Minh City University of Education Journal of Science, 21(3), 2065-2080. https://doi.org/10.54607/hcmue.js.21.3.4123(2023)
Thai, H. M., Nguyen, V. T. D., Hoang, N. P., & Tran, T. D. (2022). The boundedness of Calderón Zygmund operators of type theta on generalized weighted Lorentz spaces. Ho Chi Minh City
University of Education Journal of Science, 19(6), 844-855. https://doi.org/10.54607/hcmue.js.19.6.3362(2022)
Torchinsky, A. (1986). Real-Variable Methods in Harmonic Analysis. Academic Press.
Tran, T. D., Dao, N. A., Duong, X. T., & Le, T. N. (2024). Commutators on Spaces of Homogeneous Type in Generalized Block Spaces. The Journal of Geometric Analysis, 34(7), Article 209. https://doi.org/10.1007/s12220-024-01662-1
Uchiyama, A. (1978). On the compactness of operators of Hankel type. Tohoku Mathematical Journal, Second Series, 30(1), 163-171. https://doi.org/10.2748/tmj/1178230105
Yabuta, K. (1985). Calderón-Zygmund operators and pseudo-differential operators. Communications in Partial Differential Equations, 10(9), 1005-1022. https://doi.org/10.1007/BFb0061458