Commutators of Theta-type Generalized Calderón-Zygmund Operators on Generalized Weighted Morrey Spaces

Commutators on Generalized Weighted Morrey Spaces

Authors

  • Yusuf Ramadana Universitas Negeri Makassar
  • Syamsuddin Mas'ud Universitas Negeri Makassar

DOI:

https://doi.org/10.24252/msa.v13i1.56052

Keywords:

Commutator, generalized Calderón-Zygmund operator, generalized weighted Morery spaces, A_p weight

Abstract

In this paper, we conduct a comprehensive study on the boundedness properties of commutators generated by a BMO function and generalized Calderón-Zygmund operator. Specifically, we analyze their mapping behavior from a generalized weighted Morrey space to another generalized weighted Morrey spaces  under some conditions on the parameters. Our main objective is to establish novel and refined conditions on the pair of parameter functions  that guarantee the boundedness of these commutators on the spaces. The findings presented in this work contribute to a deeper understanding of the interplay between function spaces, weight conditions, and the structure of commutators in harmonic analysis.

Author Biographies

Yusuf Ramadana, Universitas Negeri Makassar

Mathematics

Syamsuddin Mas'ud, Universitas Negeri Makassar

Mathematics

References

Álvarez, R.J. Babgy, dan C. Pérez. (1993). "Weighted Estimates for Commutators of Linear Operators". Studia Mathematica, 104(2), 195--209.

R.R. Coifman dan Y. Meyer. (1979). "Au Delà des Opérateurs Pseudo-Différentiels". Astérisque, 57.

J. Duoandikoetxea. (2000). Fourier Analysis. American Mathematical Society, Providence.

G. Dafni, R. Gibara, dan A. Lavigne. (2020). "BMO and the John-Nirenberg Inequality on Measure Spaces". Analysis and Geometry in Metric Spaces, 8(1), 335--362.

G. Di Fazio dan M.A. Ragusa. (1991). "Commutators and Morrey Spaces". Bollettino della Unione Matematica Italiana, 7, 323--332.

C. Fefferman dan E. Stein. (1972). "H^p Spaces of Several Variables". Acta Mathematica, 129, 137--193.

K. Yabuta. (1985). "Generalizations of Calderón-Zygmund Operators". Studia Mathematica, 82(1), 17--31.

J. Garcia-Cuerva dan J.L. Rubio de Francia. (1985). Weighted Norm Inequalities and Related Topics. Elsevier Science Publishers BV, Amsterdam.

L. Grafakos. (2014). Modern Fourier Analysis (3rd Edition). Springer, New York.

V.S. Guliyev, T. Karaman, R.C. Mustafayev, dan A. Serbetci. (2014). "Commutators of Sublinear Operators Generated by Calderón-Zygmund Operator on Generalized Weighted Morrey Spaces". Czechoslovak Mathematical Journal, 64(2), 365--385.

Y. Komori dan S. Shirai. "Weighted Morrey Sspaces and Singular Integral Operator". Mathematische Nachrichten, 282(2), 219--231.

Y. Komori dan T. Mizuhara. (2003). "Notes on Commutators and Morrey Spaces". Hokkaido Mathematical Journal, 32, 345--353.

T. Mizuhara. (1993). "Boundedness of Some Classical Operators on Generalized Morrey Spaces". ICM-90 Satellite Conference Proceedings. Springer, Tokyo.

C.B. Morrey. (1938). "On the Solutions of Quasi-linear Elliptic Partial Differential Equations". Transactions of the American Mathematical Society, 43(1), 126--166.

Y. Ramadana dan H. Gunawan. (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.

Y. Sawano, G. Di Fazio, dan D.I. Hakim. (2020). Morrey Space: Introduction and Applications to Integral Operators and PDE's. CRC Press.

C. Segovia dan J.L. Torrea. (1991). "Weighted Inequalities for Commutators of Fractional and Singular Integrals". Publicacions Matemàtiques, 35, 209--235.

E.M. Stein. (1993). Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, New Jersey.

H. Wang. (2012). "Intrinsic Square Functions on the Weighted Morrey Spaces". Journal of Mathematical Analysis and Applications, 396(1), 302--314.

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Published

2025-05-30

How to Cite

[1]
Y. Ramadana and Syamsuddin Mas’ud, “Commutators of Theta-type Generalized Calderón-Zygmund Operators on Generalized Weighted Morrey Spaces: Commutators on Generalized Weighted Morrey Spaces”, MSA, vol. 13, no. 1, pp. 34–40, May 2025.

Issue

Vol. 13 No. 1 (2025): VOLUME 13 NO 1 TAHUN 2025

Section

Artikel

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