Geodesic
An intrinsic description of functions defined on a~plane convex domain and having a~prescribed order approximation by algebraic polynomials
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 14, Tome 215 (1994), pp. 217-225

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Let $0\alpha$, $0$, $m$ a positive integer, let $f$ a function defined on a plane convex domain $G$. Denote by $E_m(f,L_p(G))$ the best approximation of $f$ in $L_p(G)$ by algebraic polynomials of degree $m$. A description of functions $f\in L_p(G)$ such that inequalities hold $$ E_m(f,L_p(G))\le Cm^{-\alpha},\qquad m=1,2,\dots, $$ is given. Bibliography: 7 titles. 
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     author = {Yu. V. Netrusov},
     title = {An intrinsic description of functions defined on a~plane convex domain and having a~prescribed order approximation by algebraic polynomials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
     volume = {215},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a13/}
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Yu. V. Netrusov. An intrinsic description of functions defined on a~plane convex domain and having a~prescribed order approximation by algebraic polynomials. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 14, Tome 215 (1994), pp. 217-225. http://geodesic.mathdoc.fr/item/ZNSL_1994_215_a13/