Geodesic
Embeddings of the classes $H^\omega$
Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 713-719 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we study functions belonging to the classes $V_\varphi$ and $\Lambda BV$, which are encountered in the theory of Fourier trigonometric series. Necessary and sufficient conditions for the embedding of the classes $H^\omega$ in the classes $V_\varphi$ and $\Lambda BV$ are obtained. 
@article{MZM_1998_64_5_a7,
     author = {M. V. Medvedeva},
     title = {Embeddings of the classes $H^\omega$},
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     pages = {713--719},
     year = {1998},
     volume = {64},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a7/}
}
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M. V. Medvedeva. Embeddings of the classes $H^\omega$. Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 713-719. http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a7/

[1] Young L. C., “General inequalities for Stieltjes integrals and the convergence of Fourier series”, Math. Ann., 115:4 (1938), 581–612 | DOI | MR | Zbl

[2] Saakyan A. A., “O skhodimosti dvoinykh ryadov Fure funktsii ogranichennoi garmonicheskoi variatsii”, Izv. AN AzSSR. Matem., 1987, no. 6, 517–529

[3] Waterman D., “On convergence of Fourier series of functions of generalized bounded variation”, Studia Math., 44:2 (1972), 107–117 | MR | Zbl

[4] Hardy G. H., Littlewood J. E., “A convergence criterion for Fourier series”, Math. Z., 28:4 (1928), 612–634 | DOI | MR

[5] Ulyanov P. L., “Vlozhenie nekotorykh klassov funktsii $H^\omega_p$”, Izv. AN SSSR. Ser. matem., 32:3 (1968), 649–686 | MR | Zbl

[6] Kovacik O., “On the embedding $H^\omega\subset V_p$”, Math. Slovaca, 43:5 (1993), 573–578 | MR | Zbl

[7] Korneichuk N. P., Ekstremalnye zadachi teorii priblizheniya, Nauka, M., 1976