Geodesic
Multidimensional generalization of a~Tauberian theorem of Hardy and Littlewood
Izvestiya. Mathematics , Tome 10 (1976) no. 5, pp. 1031-1048.

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A multidimensional Tauberian theorem is established which generalizes the one-dimensional Tauberian theorem of Hardy and Littlewood. Bibliography: 6 titles. 
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     title = {Multidimensional generalization of {a~Tauberian} theorem of {Hardy} and {Littlewood}},
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V. S. Vladimirov. Multidimensional generalization of a~Tauberian theorem of Hardy and Littlewood. Izvestiya. Mathematics , Tome 10 (1976) no. 5, pp. 1031-1048. http://geodesic.mathdoc.fr/item/IM2_1976_10_5_a4/

[1] Vladimirov V. S., “Preobrazovanie Laplasa obobschennykh funktsii medlennogo rosta”, Sovremennye problemy matematiki, 1, VINITI, 1973, 61–84

[2] Vladimirov V. S., Metody teorii funktsii mnogikh kompleksnykh peremennykh, Nauka, M., 1964 | MR

[3] Khardi G., Raskhodyaschiesya ryady, IL, M., 1951

[4] Postnikov A. G., Vvedenie v analiticheskuyu teoriyu chisel, Nauka, M., 1971 | MR

[5] Fenchel W., “On cojugate convex functions”, Canad. J. Math., 1 (1949), 73–77 | MR | Zbl

[6] Vladimirov V. S., “Preobrazovanie Lezhandra vypuklykh funktsii”, Matem. zametki, 1 (1967), 675–682 | MR | Zbl