Geodesic
Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables
Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 265-302

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We obtain order-exact estimates for the best $M$-term trigonometric approximations of the Besov classes $B_{p,\theta}^r$ of periodic functions of several variables in $L_q$ with certain relations between $p$ and $q$. 
@article{IM2_2003_67_2_a3,
     author = {A. S. Romanyuk},
     title = {Best $M$-term trigonometric approximations of {Besov} classes of periodic functions of several variables},
     journal = {Izvestiya. Mathematics },
     pages = {265--302},
     publisher = {mathdoc},
     volume = {67},
     number = {2},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a3/}
}
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A. S. Romanyuk. Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables. Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 265-302. http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a3/