Startseite (L p,λ,μ,L q,λ,μ) boundedness of the G-fractional integral operator on G-Morrey spaces
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(L p,λ,μ,L q,λ,μ) boundedness of the G-fractional integral operator on G-Morrey spaces

  • Elman J. Ibrahimov EMAIL logo und Saadat A. Jafarova
Veröffentlicht/Copyright: 2. Oktober 2024
Analysis
Aus der Zeitschrift Analysis Band 45 Heft 1

Abstract

In this paper we find conditions for the boundedness of the strong and weak fractional integral and fractional maximal operator generated by Gegenbauer differential operator on G-Morrey spaces.

MSC 2020: 42B20; 42B25

References

[1] D. R. Adams, A note on Riesz potentials, Duke Math. J. 42 (1975), no. 4, 765–778. 10.1215/S0012-7094-75-04265-9Suche in Google Scholar

[2] D. R. Adams, Morrey spaces, Lect. Notes. Appl. Numer. Harmon. Anal., Springer, Cham, 2015. 10.1007/978-3-319-26681-7_13Suche in Google Scholar

[3] L. Durand, P. M. Fishbane and L. M. Simmons, Jr., Expansion formulas and addition theorems for Gegenbauer functions, J. Math. Phys. 17 (1976), no. 11, 1933–1948. 10.1063/1.522831Suche in Google Scholar

[4] V. S. Guliev and E. D. Ibragimov, Conditions for the L p , λ -boundedness of the Riesz potential generated by the Gegenbauer differential operator, Math. Notes 105 (2019), no. 9, 674–683. 10.1134/S0001434619050043Suche in Google Scholar

[5] V. S. Guliyev and J. J. Hasanov, Necessary and sufficient conditions for the boundedness of B-Riesz potential in the B-Morrey spaces, J. Math. Anal. Appl. 347 (2008), no. 1, 113–122. 10.1016/j.jmaa.2008.03.077Suche in Google Scholar

[6] V. S. Guliyev and E. J. Ibrahimov, Generalized Gegenbauer shift and some problems of the theory of approximation of functions on the metric of L 2 , λ , Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 35 (2015), no. 4, 19–51. Suche in Google Scholar

[7] V. S. Guliyev and E. J. Ibrahimov, Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces, Georgian Math. J. 25 (2018), no. 2, 235–248. 10.1515/gmj-2018-0022Suche in Google Scholar

[8] E. J. Ibrahimov, On Gegenbauer transformation on the half-line, Georgian Math. J. 18 (2011), no. 3, 497–515. 10.1515/gmj.2011.0024Suche in Google Scholar

[9] E. J. Ibrahimov and A. Akbulut, The Hardy–Littlewood–Sobolev theorem for Riesz potential generated by Gegenbauer operator, Trans. A. Razmadze Math. Inst. 170 (2016), no. 2, 166–199. 10.1016/j.trmi.2016.05.004Suche in Google Scholar

[10] E. J. Ibrahimov, V. S. Guliyev and S. A. Jafarova, Weighted boundedness of the fractional maximal operator and Riesz potential generated by Gegenbauer differential operator, Trans. A. Razmadze Math. Inst. 173 (2019), no. 3, 45–78. Suche in Google Scholar

[11] E. J. Ibrahimov, S. A. Jafarova and R. A. Bandaliyev, Boundedness criteria for the fractional integral and fractional maximal operator on Morrey spaces generated by the Gegenbauer differential operator, Math. Methods Appl. Sci. 46 (2023), no. 18, 18605–18632. 10.1002/mma.9582Suche in Google Scholar

[12] E. J. Ibrahimov, S. A. Jafarova and S. E. Ekincioglu, Maximal and potential operators associated with Gegenbauer differential operator on generalized Morrey spaces, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 46 (2020), no. 1, 129–143. 10.29228/proc.23Suche in Google Scholar

[13] B. M. Levitan, Expansion in Fourier series and integrals with Bessel functions, Uspehi Matem. Nauk (N. S.) 6 (1951), no. 2(42), 102–143. Suche in Google Scholar

[14] B. M. Levitan, Theory of Generalized Shift Operators, Nauka, Moscow, 1973. Suche in Google Scholar

[15] C. B. Morrey, Jr., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938), no. 1, 126–166. 10.1090/S0002-9947-1938-1501936-8Suche in Google Scholar

[16] J. Peetre, On the theory of p , λ spaces, J. Funct. Anal. 4 (1969), 71–87. 10.1016/0022-1236(69)90022-6Suche in Google Scholar

Received: 2024-01-27
Revised: 2024-05-02
Accepted: 2024-07-13
Published Online: 2024-10-02
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 8.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/anly-2024-0016/html
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