The Kolmogorov n-width of W_1^1[0,1] in L_q[0,1], 2<q<∞, is of order n^{-1/2} log n, settling the last open case of the classical width classification.
Kulanin, ``On the diameters of a class of functions of bounded variation in the space L_q(0,1) , 2<q< '', Russian Mathematical Surveys, 38:5 (1983), 146--147
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Kolmogorov widths of the class $W_1^1$
The Kolmogorov n-width of W_1^1[0,1] in L_q[0,1], 2<q<∞, is of order n^{-1/2} log n, settling the last open case of the classical width classification.