Geodesic
Conditions for the $L_{p,\lambda}$-Boundedness of the Riesz Potential Generated by the Gegenbauer Differential Operator
Matematičeskie zametki, Tome 105 (2019) no. 5, pp. 685-695.

Voir la notice de l'article provenant de la source Math-Net.Ru

The results obtained in this paper refine and supplement a Hardy–Littlewood–Sobolev type theorem on the boundedness of the Riesz potential generated by the Gegenbauer differential operator on the spaces $L_{p,\lambda}$ proved in an earlier paper of the second author.
Keywords: Gegenbauer differential operator, Gegenbauer potential, generalized shift operator. 
@article{MZM_2019_105_5_a3,
     author = {V. S. Guliev and E. D. Ibragimov},
     title = {Conditions for the $L_{p,\lambda}${-Boundedness} of the {Riesz} {Potential} {Generated} by the {Gegenbauer} {Differential} {Operator}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {685--695},
     publisher = {mathdoc},
     volume = {105},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a3/}
}
TY  - JOUR
AU  - V. S. Guliev
AU  - E. D. Ibragimov
TI  - Conditions for the $L_{p,\lambda}$-Boundedness of the Riesz Potential Generated by the Gegenbauer Differential Operator
JO  - Matematičeskie zametki
PY  - 2019
SP  - 685
EP  - 695
VL  - 105
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a3/
LA  - ru
ID  - MZM_2019_105_5_a3
ER  - 
%0 Journal Article
%A V. S. Guliev
%A E. D. Ibragimov
%T Conditions for the $L_{p,\lambda}$-Boundedness of the Riesz Potential Generated by the Gegenbauer Differential Operator
%J Matematičeskie zametki
%D 2019
%P 685-695
%V 105
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a3/
%G ru
%F MZM_2019_105_5_a3
V. S. Guliev; E. D. Ibragimov. Conditions for the $L_{p,\lambda}$-Boundedness of the Riesz Potential Generated by the Gegenbauer Differential Operator. Matematičeskie zametki, Tome 105 (2019) no. 5, pp. 685-695. http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a3/

[1] D. R. Adams, “A note on Riesz potential”, Duke Math. J., 42:4 (1975), 765–778 | DOI | MR

[2] V. S. Guliyev, “On maximal function and fractional integral, associated with the Bessel differential operator”, Math. Inequal. Appl., 6:2 (2003), 317–330 | MR

[3] V. S. Guliyev, J. Hasanov, “Necessary and sufficient conditions for the boundedness of $B$-Riesz potential in the $B$-Morrey spaces”, J. Math. Anal. Appl., 347:1 (2008), 113–122 | DOI | MR | Zbl

[4] V. S. Guliyev, E. J. Ibrahimov, S. Ar. Jafarova, “Gegenbauer harmonic analysis and approximation of functions on the half line”, Adv. in Anal., 2:3 (2017), 167–195 | DOI

[5] L. Durant, P. M. Fisbane, L. M. Simmons, “Expansion formulas and addition theorems for Gegenbauer functions”, J. Math. Phys., 17:11 (1976), 1933–1948 | DOI | MR

[6] B. M. Levitan, “Razlozhenie po funktsiyam Besselya v ryady i integraly Fure”, UMN, 6:2(42) (1951), 102–143 | MR | Zbl

[7] B. M. Levitan, Teoriya operatorov obobschennogo sdviga, Nauka, M., 1973 | MR

[8] M. Flensted-Jensen, T. H. Koornwinder, “The convolution structure for Jacobi function expansions”, Ark. Mat., 11 (1973), 245–262 | DOI | MR | Zbl

[9] E. J. Ibrahimov, A. Akbulut, “The Hardy–Littlewood–Sobolev theorem for Riesz poential generated by Gegenbauer operator”, Trans. A. Razmadze Math. Inst., 170:2 (2016), 166–199 | MR | Zbl