Best approximations in 𝐿¹ are near best in 𝐿^{𝑝},𝑝<1

Best approximations in $L^ 1$ are near best in $L^ p,\ p<1$
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by Lawrence G. Brown and Bradley J. Lucier PDF

Proc. Amer. Math. Soc. 120 (1994), 97-100 Request permission

We show that any best ${L^1}$ polynomial approximation to a function $f$ in ${L^p}, 0 < p < 1$, is near best in ${L^p}$.

References

best approximation operators are bounded on

Ronald A. DeVore, Björn Jawerth, and Bradley J. Lucier, Image compression through wavelet transform coding, IEEE Trans. Inform. Theory 38 (1992), no. 2, 719–746. MR 1162221, DOI 10.1109/18.119733
Ronald A. DeVore, Björn Jawerth, and Bradley J. Lucier, Surface compression, Comput. Aided Geom. Design 9 (1992), no. 3, 219–239. MR 1175287, DOI 10.1016/0167-8396(92)90019-L
Ronald A. DeVore, Björn Jawerth, and Vasil Popov, Compression of wavelet decompositions, Amer. J. Math. 114 (1992), no. 4, 737–785. MR 1175690, DOI 10.2307/2374796
Ronald A. DeVore and Vasil A. Popov, Free multivariate splines, Constr. Approx. 3 (1987), no. 2, 239–248. MR 889558, DOI 10.1007/BF01890567
Ronald A. DeVore and Vasil A. Popov, Interpolation of Besov spaces, Trans. Amer. Math. Soc. 305 (1988), no. 1, 397–414. MR 920166, DOI 10.1090/S0002-9947-1988-0920166-3