Boundedness of G-Fractional Commutators with G-BMO functions

• Autorzy: Elman Ibrahimov , Jafarova Ar. Saadat

Identyfikatory

DOI

10.14708/cm.v61i1--2.7075

• Języki publikacji: EN

Abstrakty

EN

In this paper we study (Lp,λ,ω p , Lp,λ,ωq )-boundedness of commutators of the Gegenbauer fractional integral Jα G and fractional maximal operator Mα G generated by Gegenbauer differential operator Gλ

Słowa kluczowe

EN

G-fractional commutator; G-fractional integral; G-fractional maximal operator; G-BMO space

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2023
• Tom: Vol. 61, No. 1/2
• Strony: 1--14
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Elman Ibrahimov

• Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

autor

Jafarova Ar. Saadat

• University of Economics UNEC, 6, Istiqlaliyyat str., Baku, Az1001, Azerbaijan

Bibliografia

• [1] A. M. Alphonse, An end point estimate for maximal commutators, J. Fourier Anal. Appl. 6 (2000), no. 4, 449-456, DOI 10.1007/BF02510149.
• [2] S. Chanillo, A note on commutators, Indiana Univ. Math. J. 31 (1982), 7-16, DOI 10.1512/iumj.1982.31.31002.
• [3] Y. Ding, Weighted boundedness for commutators of integral operators of fractional order with rough kernels, Beijing Shifan Daxue Xuebao 32 (1996), no. 2, 157-161; (Chinese).
• [4] L. Durand, P. M. Fishbane, and L. M. Simmons, Expansion formulas and addition theorems for Gegenbauer functions, J. Mathematical Phys. 17 (1976), no. 11, 1933-1948, DOI 10.1063/1.522831
• [5] V. S. Guliyev, S. S. Aliyev, T. Karaman, and P. Shukurov, Boundedness of sublinear operators and com mutators on generalized Morrey spaces, Integral Equations Operator Feory 71 (2011), no. 3, 327-355, DOI 10.1007/s00020-011-1904-1.
• [6] V. S. Guliyev, A. Akbulut, and Y. Y. Mammadov, Boundedness of fractional maximal operator and their higher commutators in generalized Morrey space in Carnot groups, Acta Math. Sci. Ser. B (Engl. Ed.) 33 (2013), no. 5, 1329-1346, DOI 10.1016/S0252-9602(13)60085-5.
• [7] V. Guliyev,I. Ekincioglu, E. Kaya, and Z. Safarov, Characterizationsforthe fractional maximalcommutator operator in generalized Morrey spaces on Carnot group, Integral Transforms Spec. Funct. 30 (2019), no. 6, 453-470, DOI 10.1080/10652469.2019.1581777.
• [8] E. J. Ibrahimov, V. S. Guliyev, and S. A. Jafarova, On boundedness of fractional maximal function and Riesz-Gegenbauer potential generated by Gegenbauer di×erential operator, Trans. A. Razmadze Math. Inst. 173 (2019), no. 3, 47-78.
• [9] E. Ibrahimov, On Gegenbauer transformation on the half-line, Georgian Math. J. 18 (2011), no. 3, 497-515.
• [10] E. I. Ibrahimov, G. A. Dadashova, and S. A. Jafarova, Boundedness of higher order commutators of G-fractional integral and G-fractional maximal operatorwithG-BMO functions, Trans.A. Razmadze Math. Inst. 174 (2020), no. 3, 325-341.
• [11] S. Lu, Y. Ding, and D. Yan, Singular Integrals and Related Topics, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ 2007