Geodesic
Diameters of some classes of differentiable periodic functions in the space $L$
Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 531-543

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In this paper, diameters in the sense of A. N. Kolmogorov are found for the class of $2\pi$-periodic functions $W^{(r)}H_\omega$ in the space $L$, that is, $d_{2n-1}(W^{(r)}H_\omega, L)$, where $\omega(t)$ is an upper-convex regular modulus of continuity ($r,n=1,2,\dots$). An estimate from below is found for diameters in the sense of I. M. Gel'fand, that is, $d^{2n-1}(W^{(r)}H_\omega, L)$ 
@article{MZM_1975_17_4_a4,
     author = {V. P. Motornyi and V. I. Ruban},
     title = {Diameters of some classes of differentiable periodic functions in the space $L$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {531--543},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a4/}
}
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V. P. Motornyi; V. I. Ruban. Diameters of some classes of differentiable periodic functions in the space $L$. Matematičeskie zametki, Tome 17 (1975) no. 4, pp. 531-543. http://geodesic.mathdoc.fr/item/MZM_1975_17_4_a4/