Geodesic
Weighted estimates of multidimensional singular integrals generated by the generalized shift operator
Sbornik. Mathematics, Tome 77 (1994) no. 1, pp. 37-55 
I. A. Aliev; A. D. Gadzhiev. Weighted estimates of multidimensional singular integrals generated by the generalized shift operator. Sbornik. Mathematics, Tome 77 (1994) no. 1, pp. 37-55. http://geodesic.mathdoc.fr/item/SM_1994_77_1_a3/
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     title = {Weighted estimates of multidimensional singular integrals generated by the~generalized shift operator},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Sufficient conditions on weights are found that ensure that a multidimensional singular integral operator generated by the generalized shift operator acts boundedly from one weighted $L_p$-space into another. It is shown that in some cases the conditions are sharp.

[1] Klyuchantsev M. I., “O singulyarnykh integralakh, porozhdennykh operatorom obobschennogo sdviga, I”, Sib. matem. zhurn., 11:4 (1970), 810–821 | MR | Zbl

[2] Kipriyanov I. A., Klyuchantsev M. I., “O singulyarnykh integralakh, porozhdennykh operatorom obobschennogo sdviga, II”, Sib. matem. zhurn., 11:5 (1970), 1060–1083 | MR | Zbl

[3] Stein E. M., “Note on singular integrals”, Proc. Amer. Math. Soc., 8:2 (1957), 250–254 | DOI | MR | Zbl

[4] Dynkin E. M., Osilenker B. P., “Vesovye otsenki singulyarnykh integralov i ikh prilozheniya”, Itogi nauki i tekhniki. Matematicheskii analiz, 21, VINITI, M., 1983, 42–129 | MR

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

[6] Mazya V. G., Prostranstva S.L.Soboleva, Izd-vo Leningr. un-ta, L., 1985 | MR | Zbl

[7] Guseinov E. G., “Singulyarnye integraly v prostranstvakh funktsii, summiruemykh s monotonnym vesom”, Matem. sb., 132(174):1 (1987), 28–44 | MR | Zbl

[8] Chen Yung-ming, “Theorems of asymptotic approximations”, Math. Ann., 140:5 (1960), 360–407 | DOI | MR | Zbl

[9] Dzhanelidze O. P., “Ob ogranichennosti mnogomernogo singulyarnogo operatora v prostranstvakh s vesom”, Soobsch. AN GSSR, 87:2 (1977), 301–303 | MR