Geodesic
On the approximation by algebraic polynomials of functions of class~$L^p$, $0$
Izvestiya. Mathematics , Tome 11 (1977) no. 3, pp. 613-623.

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In the article, Whitney's inequality $$ E_{k-1}(f;[a,b])\leqslant M_k\omega_k\biggl(\frac{b-a}k,f\biggr) $$ for bounded functions $f$ on $[a,b]$ is extended to the case $f\in L^p(a,b)$ for $0$. Bibliography: 10 titles. 
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È. A. Storozhenko. On the approximation by algebraic polynomials of functions of class~$L^p$, $0

[1] Whitney H., “On functions with bounded $n$-th differences”, J. Math. Pures Appl., 36:9 (1957), 67–95 | MR | Zbl

[2] Whitney H., “On bounded functions with bounded $n$-th differences”, Proc. Amer. Math. Soc., 10:3 (1959), 480–481 | DOI | MR | Zbl

[3] Brudnyi Yu. A., “Ob odnoi teoreme lokalnykh nailuchshikh priblizhenii”, Uch. zap. Kazanskogo un-ta, 124, no. 6, 1964, 43–49 | MR

[4] Alberg Dzh., Nilson E., Uolsh Dzh., Teoriya splainov i ee prilozheniya, Mir, M., 1972 | MR | Zbl

[5] Subbotin Yu. N., “Ekstremalnye zadachi funktsionalnoi interpolyatsii i interpolyatsionnye v srednem splainy”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 138, 1975, 118–173 | MR | Zbl

[6] Brudnyi Yu. A. i Gopengauz I. E., “Priblizhenie kusochno-polinomialnymi funktsiyami”, Izv. AN SSSR. Seriya matem., 27 (1963), 723–746 | MR | Zbl

[7] Stechkin S. B., “Zamechanie k teoreme Dzheksona”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 88, 1967, 17–19 | Zbl

[8] Timan A. F., Teoriya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960

[9] Ulyanov P. L., “Teoremy vlozheniya i sootnosheniya mezhdu nailuchshimi priblizheniyami v raznykh metrikakh”, Matem. sb., 81(12) (1970), 104–131

[10] Storozhenko E. A., Krotov V, G., Osvald P., “Pryamye i obratnye teoremy tipa Dzheksona v prostranstvakh $L^p$, $0

1$”, Matem. sb., 98(140) (1975), 395–415 | MR | Zbl